Makrides et al. (25) Double-blind, placebo-controlled, randomized 2399 (n = 1197 supplemented, n = 1202 placebo; 726 children were followed up with) DHA (fish-oil capsules providing 800 mg/d DHA) Supplementation did not result in lower levels of postpartum depression in mothers or improved cognitive and language development in offspring during early childhood

16. Saito Y, Yokoyama M, Origasa H, Matsuzaki M, Matsuzawa Y, Ishikawa Y, Oikawa S, Sasaki J, Hishida H, Itakura H, et al. Effects of EPA on coronary artery disease in hypercholesterolemic patients with multiple risk factors: sub-analysis of primary prevention cases from the Japan EPA Lipid Intervention Study (JELIS). Atherosclerosis. 2008;200:135–40. [PubMed]
For rheumatoid arthritis, one systematic review found consistent, but modest, evidence for the effect of marine n−3 PUFAs on symptoms such as "joint swelling and pain, duration of morning stiffness, global assessments of pain and disease activity" as well as the use of non-steroidal anti-inflammatory drugs.[35] The American College of Rheumatology has stated that there may be modest benefit from the use of fish oils, but that it may take months for effects to be seen, and cautions for possible gastrointestinal side effects and the possibility of the supplements containing mercury or vitamin A at toxic levels. The National Center for Complementary and Integrative Health has concluded that "[n]o dietary supplement has shown clear benefits for rheumatoid arthritis", but that there is preliminary evidence that fish oil may be beneficial, but needs further study.[36]

Saito, Y., Yokoyama, M., Origasa, H., Matsuzaki, M., Matsuzawa, Y., Ishikawa, Y., Oikawa, S., Sasaki, J., Hishida, H., Itakura, H., Kita, T., Kitabatake, A., Nakaya, N., Sakata, T., Shimada, K., and Shirato, K. Effects of EPA on coronary artery disease in hypercholesterolemic patients with multiple risk factors: sub-analysis of primary prevention cases from the Japan EPA Lipid Intervention Study (JELIS). Atherosclerosis 2008;200(1):135-140. View abstract.

McNamara, R. K., Able, J., Jandacek, R., Rider, T., Tso, P., Eliassen, J. C., Alfieri, D., Weber, W., Jarvis, K., DelBello, M. P., Strakowski, S. M., and Adler, C. M. Docosahexaenoic acid supplementation increases prefrontal cortex activation during sustained attention in healthy boys: a placebo-controlled, dose-ranging, functional magnetic resonance imaging study. Am J Clin Nutr 2010;91(4):1060-1067. View abstract.
Five studies with 7 data sets recruited participants without specific clinical conditions.36,47,51,55,60 The main results revealed that there was no significant difference in the association of treatment with reduced anxiety symptoms between patients receiving omega-3 PUFA treatment and those not receiving it (k, 5; Hedges g, –0.008; 95% CI, –0.266 to 0.250; P = .95) (Figure 3A). Fourteen studies with 14 data sets recruited participants with specific clinical diagnoses.33-35,48-50,52-54,56-59,61 The main results revealed a significantly greater association of treatment with reduced anxiety symptoms in patients receiving omega-3 PUFA treatment than in those not receiving it (k, 14; Hedges g, 0.512; 95% CI, 0.119-0.906; P = .01) (Figure 3A). Furthermore, according to the interaction test, the association of omega-3 PUFA treatment with reduced anxiety symptoms was significantly stronger in subgroups with specific clinical diagnoses than in subgroups without specific clinical conditions (P = .03).

Smithers, L. G., Collins, C. T., Simmonds, L. A., Gibson, R. A., McPhee, A., and Makrides, M. Feeding preterm infants milk with a higher dose of docosahexaenoic acid than that used in current practice does not influence language or behavior in early childhood: a follow-up study of a randomized controlled trial. Am J Clin Nutr 2010;91(3):628-634. View abstract.
The American Heart Association (AHA) has made recommendations for EPA and DHA due to their cardiovascular benefits: individuals with no history of coronary heart disease or myocardial infarction should consume oily fish two times per week; and "Treatment is reasonable" for those having been diagnosed with coronary heart disease. For the latter the AHA does not recommend a specific amount of EPA + DHA, although it notes that most trials were at or close to 1000 mg/day. The benefit appears to be on the order of a 9% decrease in relative risk.[106] The European Food Safety Authority (EFSA) approved a claim "EPA and DHA contributes to the normal function of the heart" for products that contain at least 250 mg EPA + DHA. The report did not address the issue of people with pre-existing heart disease. The World Health Organization recommends regular fish consumption (1-2 servings per week, equivalent to 200 to 500 mg/day EPA + DHA) as protective against coronary heart disease and ischaemic stroke.
Age-related macular degeneration (AMD) is an eye disease that can cause vision loss in older people. Two major National Institutes of Health (NIH)-sponsored studies, called Age-Related Eye Disease Study (AREDS) and Age-Related Eye Disease Study 2 (AREDS2), showed that dietary supplements containing specific combinations of vitamins, antioxidants, and zinc helped slow the progression of AMD in people who were at high risk of developing the advanced stage of this disease. AREDS2, which had more than 4,000 participants and was completed in 2013, also tested EPA and DHA. The results showed that adding these omega-3s to the supplement formulation didn’t provide any additional benefits. Other, smaller studies of omega-3 supplements also haven’t shown them to have a beneficial effect on the progression of AMD. 
People used to believe that osteoporosis and osteoarthritis were the result of aging and reduced intake of calcium and milk products. Science has now shown that these bone and joint disorders are, in part, due to inflammation. Because of this, bones and joints are prime targets for the anti-inflammatory properties of omega-3 oils from both fish and krill.
Oftentimes this could be a result of poor body composition, poor activity levels, or other things, like a low-quality diet. Now, for other people, I do think it’s the case that for people who do not eat fish and for people whose animal products, especially their eggs, are mostly from animals fed grains rather than pasture-raised animals or who don’t eat eggs, I think in those cases there is an argument for fish oil in the sense that those people are probably not going to get enough omega-3 fatty acids, but the better argument might be: Eat pastured eggs or eat fish. Even eating an oily fish like salmon once or twice a week is probably good enough to provide the omega-3 fatty acids that you need. Eating some pastured egg yolks every day is probably good enough to provide for the omega-3 fatty acids that you need.
Fish oil supplement studies have failed to support claims of preventing heart attacks or strokes.[3][4][5][6] Earlier, in 2007, the American Heart Association had recommended the consumption of 1 gram of fish oil daily, preferably by eating fish, for patients with coronary artery disease, but cautioned pregnant and nursing women to avoid eating fish with high potential for mercury contaminants including mackerel, shark, and swordfish.[32] (Optimal dosage was related to body weight.)

Fish oil has been shown to have a direct electrophysiological effect on the myocardium. Initial experience with animal ischemia models demonstrated that the ventricular fibrillation threshold was increased in both animals fed or infused with omega-3 FA.23,24 This progressed to a demonstration, on a cellular and ion channel level, that omega-3 FA reduce both sodium currents and L-type calcium currents.25–29 It is hypothesized that during ischemia, a reduction in the sodium ion current protects hyperexcitable tissue, and a reduction in the calcium ion current reduces arrhythmogenic depolarizing currents.30
The bottom line of all that is that there was no clear health benefit from consuming omega-3 fatty acids in food or supplements. There was a suggestion of a possible benefit from LCn3 on cardiac events, but this did not hold up when they took into consideration the quality of the evidence. The better trials, with less risk of bias, tended to be negative.
van der Meij, B. S., Langius, J. A., Smit, E. F., Spreeuwenberg, M. D., von Blomberg, B. M., Heijboer, A. C., Paul, M. A., and van Leeuwen, P. A. Oral nutritional supplements containing (n-3) polyunsaturated fatty acids affect the nutritional status of patients with stage III non-small cell lung cancer during multimodality treatment. J.Nutr. 2010;140(10):1774-1780. View abstract.
A tremendous body of research has been conducted on these important nutrients since it was first discovered in the 1950s that fish oil offered many health benefits and that these benefits were attributable to a type of polyunsaturated fat called omega-3. Despite the volumes of research on omega-3s, it is only in recent years (within the last 15 years or so) that the actions of EPA and DHA have come to be understood individually. Researchers now often investigate the actions of EPA and DHA individually rather than together, no longer simply under the generic label omega-3 as they are widely referred to.
The effect of fish oil on incident atrial fibrillation has not been studied in large randomized trials, and observational population-based trials show mixed results. The Danish Diet, Cancer and Health Study, and the Rotterdam Study followed 47,000 and 5100 middle-aged adults, respectively.45,46 Neither study found that the consumption of fish oil affected the incidence of atrial fibrillation. Similar findings were seen in the Women’s Health Initiative where there was no association between fish and omega-3 FA intake regarding incident atrial fibrillation.47 However, in a 12-year prospective, observational study of 4815 adults over the age of 65, daily fish consumption was associated with a 31% risk reduction in incident atrial fibrillation.48

Depression. There is inconsistent evidence on the effect of taking fish oil for depression. Some research shows that taking fish oil along with an antidepressant might help improve symptoms in some people. Other research shows that taking fish oil does not improve depression symptoms. The conflicting results may be due to the amount of EPA and DHA in the supplement or the severity of depression before treatment.