I now suspect that those thousands of gel-covered capsules I’ve swallowed over the years may have done little more than enrich the pockets of supplement producers and sellers. A number of extensive analyses have been conducted, some supporting and others refuting the value of fish oils to the cardiovascular system, along with studies of other purported health benefits that also have had mixed results.

On September 8, 2004, the U.S. Food and Drug Administration gave "qualified health claim" status to EPA and DHA omega−3 fatty acids, stating, "supportive but not conclusive research shows that consumption of EPA and DHA [omega−3] fatty acids may reduce the risk of coronary heart disease".[98] This updated and modified their health risk advice letter of 2001 (see below).
LCn3s are long chain fatty acids from fish, including eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA). ALA is plant-based omega 3-alpha‐linolenic acid. Fatty acids are essentially chains of carbon atoms with an OOH group at one end. The available binding sites on the carbon atoms are filled with hydrogen atoms. If every binding site is occupied with a hydrogen, that is a saturated fatty acid. If instead of hydrogen atoms there is a double bond between two adjacent carbon atoms, that is an unsaturated fatty acid. If there are multiple double bonds, that is polyunsaturated. Omega 3 fatty acids are unsaturated, with a double bond between the third and fourth carbon atoms from the end opposite the OOH group.
Fish oils might slow blood clotting. Taking fish oils along with medications that also slow clotting might increase the chances of bruising and bleeding.Some medications that slow blood clotting include aspirin, clopidogrel (Plavix), diclofenac (Voltaren, Cataflam, others), ibuprofen (Advil, Motrin, others), naproxen (Anaprox, Naprosyn, others), dalteparin (Fragmin), enoxaparin (Lovenox), heparin, warfarin (Coumadin), and others.
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.
A 2012 study involved children from 6 to 12 years of age with ADHD who were being treated with methylphenidate and standard behavior therapy for more than six months. The parents of these children reported no improvement in behavior and academic learning using these standard treatments. The researchers randomly gave some of the children an omega-3 and omega-6 acid supplementation or a placebo. They found “statistically significant improvement” for the omega group in the following categories: restlessness, aggressiveness, completing work and academic performance. (5)
Heterogeneity was examined using the Q statistic and the corresponding P values,41 and the I2 statistic was used to evaluate the proportion of variation resulting from among-study differences. Any possible publication bias was detected with both funnel plots and Egger regression in the main part of the meta-analysis.42 By using Duval and Tweedie’s trim-and-fill test, we adjusted the effect sizes for potential publication bias if there was evidence of publication bias detected by this test in the Comprehensive Meta-analysis statistical software, version 3.43 To investigate the potential confounding effects of any outliers within the recruited studies, sensitivity testing was conducted with the 1-study removal method to detect the potential outliers.44
There have been numerous clinical trials looking mainly at death, stroke, and cardiac outcomes related to omega 3 consumption, either in food or in supplements. Now the Cochrane Library has published the largest systematic review of these studies to date. Unfortunately, the review shows little benefit from consuming omega 3 fatty acid. This is a fairly extensive review with good statistical power:

Weak bones (osteoporosis). Research suggests that taking fish oil alone or together with calcium and evening primrose oil slows the rate of bone loss and increases bone density at the thigh bone (femur) and spine in elderly people with osteoporosis. But taking fish oil does not slow bone loss in older people with osteoarthritis in the knee but without weak bones.

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. 

^ Jump up to: a b Casula M, Soranna D, Catapano AL, Corrao G (August 2013). "Long-term effect of high dose omega-3 fatty acid supplementation for secondary prevention of cardiovascular outcomes: A meta-analysis of randomized, placebo controlled trials [corrected]". Atherosclerosis. Supplements. 14 (2): 243–51. doi:10.1016/S1567-5688(13)70005-9. PMID 23958480.
Omega−3 fatty acids are important for normal metabolism.[8] Mammals are unable to synthesize omega−3 fatty acids, but can obtain the shorter-chain omega−3 fatty acid ALA (18 carbons and 3 double bonds) through diet and use it to form the more important long-chain omega−3 fatty acids, EPA (20 carbons and 5 double bonds) and then from EPA, the most crucial, DHA (22 carbons and 6 double bonds).[8] The ability to make the longer-chain omega−3 fatty acids from ALA may be impaired in aging.[9][10] In foods exposed to air, unsaturated fatty acids are vulnerable to oxidation and rancidity.[11]

Fish oil supplements came under scrutiny in 2006, when the Food Standards Agency in the UK and the Food Safety Authority of Ireland reported PCB levels that exceeded the European maximum limits in several fish oil brands,[60][61] which required temporary withdrawal of these brands. To address the concern over contaminated fish oil supplements, the International Fish Oil Standards (IFOS) Program, a third-party testing and accreditation program for fish oil products, was created by Nutrasource Diagnostics Inc. in Guelph, Ontario, Canada.[62]
Omega−3 fatty acids, also called ω−3 fatty acids or n−3 fatty acids,[1] are polyunsaturated fatty acids (PUFAs).[2][3] The fatty acids have two ends, the carboxylic acid (-COOH) end, which is considered the beginning of the chain, thus "alpha", and the methyl (-CH3) end, which is considered the "tail" of the chain, thus "omega". One way in which a fatty acid is named is determined by the location of the first double bond, counted from the tail, that is, the omega (ω-) or the n- end. Thus, in omega-3 fatty acids the first double bond is between the third and fourth carbon atoms from the tail end. However, the standard (IUPAC) chemical nomenclature system starts from the carboxyl end.
Omega 3 fatty acids—found in supplements and naturally in some foods like certain fish, and nuts and seeds—have long been touted for their health benefits, especially heart health. Yet, a lot is still unknown, including whether it's better to get your omega 3 fats from pills or in food—and the debate continues regarding how much they may actually help you avoid heart disease.
High triglycerides. Most research shows that fish oil from supplements and food sources can reduce triglyceride levels. The effects of fish oil appear to be the greatest in people who have very high triglyceride levels. Also the amount of fish oil consumed seems to directly affect how much triglyceride levels are reduced. Some fish oil supplements including Lovaza, Omtryg, and Epanova have been approved by the FDA to lower triglycerides.