Arsenault, L. N., Matthan, N., Scott, T. M., Dallal, G., Lichtenstein, A. H., Folstein, M. F., Rosenberg, I., and Tucker, K. L. Validity of estimated dietary eicosapentaenoic acid and docosahexaenoic acid intakes determined by interviewer-administered food frequency questionnaire among older adults with mild-to-moderate cognitive impairment or dementia. Am J Epidemiol 7-1-2009;170(1):95-103. View abstract.
Fatty predatory fish like sharks, swordfish, tilefish, and albacore tuna may be high in omega-3 fatty acids, but due to their position at the top of the food chain, these species may also accumulate toxic substances through biomagnification. For this reason, the United States Environmental Protection Agency recommends limiting consumption (especially for women of childbearing age) of certain (predatory) fish species (e.g. albacore tuna, shark, king mackerel, tilefish and swordfish) due to high levels of the toxic contaminant mercury. Dioxin, PCBs and chlordane are also present.[13] Fish oil is used as a component in aquaculture feed. More than 50 percent of the world's fish oil used in aquaculture feed is fed to farmed salmon.[14]
(How much omega-3 is necessary to increase one’s omega-3 index?  Studies show it can take between 1800 – 2000 mg of EPA/DHA daily to move a person’s index by 4 – 5 percentage points (12). Importantly, this is a much larger dose than you’d get swallowing one or two regular fish oil capsules and could well explain why many traditional omega-3 products fail to deliver results.)

Three randomized trials assessing more than 600 patients with known malignant ventricular arrhythmia were carried out under the protection of implanted cardioverter defibrillator (ICD) therapy.41–43 In all 3 of the trials, 75% of the patients had ischemic heart disease, survived ventricular tachycardia or ventricular fibrillation and were randomized to 1 to 3 g/d of fish oil. In the first trial of its kind, 402 patients with ICDs were randomized to either a fish oil or an olive oil supplement.41 Although statistical significance was not reached, after approximately 1 year the primary end-point of time to first ICD cardioversion for ventricular tachycardia or fibrillation or death from any cause was longer in the fish oil group. This finding was not replicated in a trial of 200 patients who were randomized to either fish oil or a placebo and followed for a median of approximately 2 years.42 In fact, time to first ICD cardioversion was not changed and the incidence of recurrent ventricular tachycardia and fibrillation was more common in the group assigned to fish oil. In the largest trial, 546 patients were randomized to supplemental fish oil or a placebo and were followed for a mean period of 1 year.43 The primary outcome of the rate of ICD cardioversion or all-cause mortality was not reduced. It was concluded in a recent meta-analysis of these trials that fish oil did not have a protective effect.44

Human growth and intellectual development – DHA plays a very important role during fetal development, early infancy and old age. High concentrations of DHA are found in the brain and increase 300 to 500 percent in an infant’s brain during the last trimester of pregnancy. Adding DHA to a pregnant mother’s diet may be beneficial for the fetus’s brain development. Elderly people should also take EPA DHA, because as we get older, our bodies form less EPA and DHA, which may cause less mental focus and cognitive function. Taking EPA DHA also may help with mental abnormalities, such as Alzheimer’s disease and dementia.
The conversion of ALA to EPA and further to DHA in humans has been reported to be limited, but varies with individuals.[79][80] Women have higher ALA-to-DHA conversion efficiency than men, which is presumed[81] to be due to the lower rate of use of dietary ALA for beta-oxidation. One preliminary study showed that EPA can be increased by lowering the amount of dietary linoleic acid, and DHA can be increased by elevating intake of dietary ALA.[82]
What's more, ALA is just a precursor to EPA and DHA. You need certain enzymes to elongate and desaturate ALA so it can become long-chained omega-3s. Unfortunately, this does not work in some people, particularly those who are deficient in certain vitamins and minerals, leading to very low conversion rates – only 1 percent of ALA is converted to EPA/DHA. In some, the conversion can even dip as low as 0.1 to 0.5 percent!

Cancer. Research on the effects of fish oil in preventing cancer has produced conflicting results. Some population research suggests that eating fish or having higher blood levels of omega-3 fatty acids from fish oil is linked to a lower risk of different cancers, including oral cancer, pharyngeal cancer, esophageal cancer, colon cancer, rectal cancer, breast cancer, ovarian cancer, and prostate cancer. But other research suggests that eating fish does not reduce the risk of cancer.
Several large studies have linked higher blood levels of long-chain omega-3s with higher risks of prostate cancer. However, other research has shown that men who frequently eat seafood have lower prostate cancer death rates and that dietary intakes of long-chain omega-3s aren’t associated with prostate cancer risk. The reason for these apparently conflicting findings is unclear. 

Some studies suggest that people who get higher amounts of omega-3s from foods and dietary supplements may have a lower risk of breast cancer and perhaps colorectal cancer. More research is needed to confirm this possible link. Whether omega-3s affect the risk of other cancers is not clear. Clinical trials to examine this possibility are in progress.
Keep in mind that APA found in plant-based foods takes a lot of energy for your body to convert to EPA and DHA. I understand that many people following a vegan diet struggle with the concept of fish oil or eating fish, but animal products contain the necessary omega-3 fatty acids to allow your body to absorb and synthesize what you take in. However, there are plant-based options — you’ll just need more APA because of the way your body processes the medium-chain fatty acid.
Good points, Miroslav. Focusing on your 4th point, with so many different formulations on the market that contain various preservatives, only looking at the blood levels of omega-3’s as the flag for increased risk for prostate cancer tends to ignore the fact that certain populations in coastal regions maintain a diet high in omega fish oils and don’t have a marked increase level of prostate cancer, pointing to the fact that another agent may be to blame here.

Gerber, J. G., Kitch, D. W., Fichtenbaum, C. J., Zackin, R. A., Charles, S., Hogg, E., Acosta, E. P., Connick, E., Wohl, D., Kojic, E. M., Benson, C. A., and Aberg, J. A. Fish oil and fenofibrate for the treatment of hypertriglyceridemia in HIV-infected subjects on antiretroviral therapy: results of ACTG A5186. J.Acquir.Immune.Defic.Syndr. 4-1-2008;47(4):459-466. View abstract.
Fish oils rich in omega 3 fatty acids help improve fertility and cell division. Preliminary research conducted on animals has shown that when males are fed a diet containing fish oil, the quality of the sperm is enhanced. After ejaculation, the sperm has increased survival against lipid peroxidative attacks in the female genital tract, thereby increasing the chances of conception. On the other hand, similar animal studies have shown inhibition in the synthesis of prostaglandin E and prostaglandin F, which are produced in large quantities by human seminal vesicles. The research, however, found no impact on the count and mobility of sperm.
AD is a devastating disease for which there are limited treatment options and no cure. Memory loss is an early indicator of the disease, which is progressive, and leads to the inability of the patient to care for him- or herself and eventually to death (47). Currently, the number of individuals with AD is estimated to be 26.6 million and is expected to increase to 106.2 million by 2050 (48). There have been many studies conducted regarding the use of omega-3 fatty acid supplementation and AD (Table 2). DHA is present in large amounts in neuron membrane phospholipids, where it is involved in proper function of the nervous system, which is why it is thought to play a role in AD (49). A case-control study consisting of 148 patients with cognitive impairment [Mini-Mental State Examination (MMSE) score <24] and 45 control patients (MMSE score ≥24) showed that serum cholesteryl ester-EPA and -DHA levels were significantly lower (P < 0.05 and P < 0.001, respectively) in all MMSE score quartiles of patients with AD compared with control values (49). Another study found that a diet characterized by higher intakes of foods high in omega-3 fatty acids (salad dressing, nuts, fish, tomatoes, poultry, cruciferous vegetables, fruits, dark and green leafy vegetables), and a lower intake of foods low in omega-3 fatty acids (high-fat dairy products, red meat, organ meat, butter) was strongly associated with a lower AD risk (50). Image analysis of brain sections of an aged AD mouse model showed that overall plaque burden was significantly reduced by 40.3% in mice with a diet enriched with DHA (P < 0.05) compared with placebo. The largest reductions (40–50%) were seen in brain regions that are thought to be involved with AD, the hippocampus and parietal cortex (51). A central event in AD is thought to be the activation of multiple inflammatory cells in the brain. Release of IL-1B, IL-6, and TNF α from microglia cells may lead to dysfunction of the neurons in the brain (52). In 1 study, AD patients treated with EPA+DHA supplementation increased their plasma concentrations of EPA and DHA, which were associated with reduced release of inflammatory factors IL-1B, IL-6, and granulocyte colony–stimulating factor from peripheral blood mononuclear cells (53).
Khandelwal, S., Demonty, I., Jeemon, P., Lakshmy, R., Mukherjee, R., Gupta, R., Snehi, U., Niveditha, D., Singh, Y., van der Knaap, H. C., Passi, S. J., Prabhakaran, D., and Reddy, K. S. Independent and interactive effects of plant sterols and fish oil n-3 long-chain polyunsaturated fatty acids on the plasma lipid profile of mildly hyperlipidaemic Indian adults. Br.J.Nutr. 2009;102(5):722-732. View abstract.
Despite this one study, you should still consider eating fish and other seafood as a healthy strategy. If we could absolutely, positively say that the benefits of eating seafood comes entirely from omega-3 fats, then downing fish oil pills would be an alternative to eating fish. But it’s more than likely that you need the entire orchestra of fish fats, vitamins, minerals, and supporting molecules, rather than the lone notes of EPA and DHA.

A scientific review in 2014 evaluated study findings on omega-3 intake in relation to the prevention and treatment of breast cancer, the most prevalent cancer among women. The review found that EPA and DHA, as well as ALA, can differentially inhibit breast tumor development. According to this review, there is solid evidence to support the use of omega-3s as “a nutritional intervention in the treatment of breast cancer to enhance conventional therapeutics, or potentially lowering effective doses.” (16) Additionally, a 2016 study found that “very high fish consumption in early adulthood to midlife may be associated with decreased risk of breast cancer.” (17)
Full citation: Abdelhamid AS, Brown TJ, Brainard JS, Biswas P, Thorpe GC, Moore HJ, Deane KHO, AlAbdulghafoor FK, Summerbell CD, Worthington HV, Song F, Hooper L. Omega 3 fatty acids for the primary and secondary prevention of cardiovascular disease. Cochrane Database of Systematic Reviews 2018, Issue 7. Art. No.: CD003177. DOI: 10.1002/14651858.CD003177.pub3.
Another study conducted by researchers at Rhode Island Hospital examined the relationship between fish oil supplementation and indicators of cognitive decline. The subjects of the study were older adults: 229 cognitively normal individuals, 397 patients with mild cognitive impairment and 193 patients with Alzheimer’s disease. They were assessed with neuropsychological tests and brain magnetic resonance imaging every six months while taking fish oil supplements. The study found that the adults taking fish oil (who had not yet developed Alzheimer’s and did not have genetic risk factor for developing Alzheimer’s known as APOE ε4) experienced significantly less cognitive decline and brain shrinkage than adults not taking fish oil. (9)
The ultimate goal of using omega-3 fatty acids is the reduction of cellular inflammation. Since eicosanoids derived from arachidonic acid (AA), an omega-6 fatty acid, are the primary mediators of cellular inflammation, EPA becomes the most important of the omega-3 fatty acids to reduce cellular inflammation for a number of reasons. First, EPA is an inhibitor of the enzyme delta-5-desaturase (D5D) that produces AA (1). The more EPA you have in the diet, the less AA you produce. This essentially chokes off the supply of AA necessary for the production of pro-inflammatory eicosanoids (prostaglandins, thromboxanes, leukotrienes, etc.). DHA is not an inhibitor of this enzyme because it can’t fit into the active catalytic site of the enzyme due to its larger spatial size. As an additional insurance policy, EPA also competes with AA for the enzyme phospholipase A2 necessary to release AA from the membrane phospholipids (where it is stored). Inhibition of this enzyme is the mechanism of action used by corticosteroids. If you have adequate levels of EPA to compete with AA (i.e. a low AA/EPA ratio), you can realize many of the benefits of corticosteroids but without their side effects. That’s because if you don’t release AA from the cell membrane then you can’t make inflammatory eicosanoids. Because of its increased spatial dimensions, DHA is not a good competitor of phospholipase A2 relative to EPA. On the other hand, EPA and AA are very similar spatially so they are in constant competition for the phospholipase A2 enzyme just as both fatty acids are in constant competition for the delta-5 desaturase enzyme. This is why measuring the AA/EPA ratio is such a powerful predictor of the state of cellular inflammation in your body.

The evidence that fish oil consumption should be used for primary prevention of CAD is based on observational studies. The only randomized trial for primary prevention, the JELIS trial, showed a moderate relative risk reduction and was conducted in a very specific group. Nevertheless, to date, there has been no strong signal suggesting any serious adverse effects of having high DHA and EPA oils in the diet. We agree with the national guidelines that one should consume moderate amounts of fish oil— either in supplement or through the dietary intake of fatty fish with low mercury levels.
Heart disease. Eating fish can be effective for keeping people with healthy hearts free of heart disease. People who already have heart disease might also be able to lower their risk of dying from heart disease by eating fish. The picture is less clear for fish oil supplements. For people who already take heart medications such as a "statin" and those who already eat a decent amount of fish, adding on fish oil might not offer any additional benefit.