Since EPA and DHA are both essential for health and appear together in nature, many studies have attempted to treat clinical conditions with combined EPA and DHA oils, but the outcomes have been varied, contradictory and disappointing. Consequently, researchers have started to investigate the individual actions of EPA and DHA in isolation, in numerous health conditions where an omega-3 deficiency is related to symptoms or known to play a causative role. The emerging evidence shows marked differences between how these two fatty acids affect us – not just at the cellular level but also the body as a whole.
The hypotriglyceridemic effect of fish oil is well established and is related to both dose and baseline triglyceride level. Patients with triglycerides <90 mg/dL will be negligibly affected unless very high doses of omega-3 FA are used.67,68 However, in patients with triglycerides >200 mg/dL, who are treated with 4 g/d of fish oil, a 30% reduction in triglycerides is expected.17,69 For patients with triglycerides >500 mg/dL who are at risk for pancreatitis, the National Cholesterol Education Program Adult Treatment Panel III guidelines recommend using fish oil supplements as an adjunctive therapy to fibrates and nicotinic acid.70 Lovaza capsules have been shown to be effective, safe, and comparable to gemfibrozil in treating triglycerides at this range.71,72 The official label recommendation for Lovaza is for patients with triglycerides >500 mg/dL.73
One meta-analysis concluded that omega−3 fatty acid supplementation demonstrated a modest effect for improving ADHD symptoms.[39] A Cochrane review of PUFA (not necessarily omega−3) supplementation found "there is little evidence that PUFA supplementation provides any benefit for the symptoms of ADHD in children and adolescents",[40] while a different review found "insufficient evidence to draw any conclusion about the use of PUFAs for children with specific learning disorders".[41] Another review concluded that the evidence is inconclusive for the use of omega−3 fatty acids in behavior and non-neurodegenerative neuropsychiatric disorders such as ADHD and depression.[42]
A certain kidney disease called IgA nephropathy. Some research shows that long-term but not short-term use of fish oil can slow the loss of kidney function in high-risk patients with IgA nephropathy. Fish oil might have greater effects when taken at higher doses. Also, it might be most effective in people with IgA nephropathy who have higher levels of protein in the urine.

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:

Omega-3 is a group of long-chain polyunsaturated fatty acids, perhaps most notably found in fatty fish. As science parses the biological actions of nutrients, it turns out that omega-3 fats do many good things for the body and the brain. Known as an "essential" fatty acid, meaning the body must take it in from food sources, omega-3 is important to human metabolism.
We’ve written about the dose necessary to achieve measurable benefits before. However, a person’s actual omega-3 intake can be tricky to estimate. Even if you eat at least two servings of fatty fish per week, as the American Heart Association recommends (10), your fish might contain more or less omega-3s depending on the fish species, the time of year, and how you cook it. Even taking fish oil supplements isn’t always straightforward, as dose can be impacted by numerous bioavailability factors, as well as genetics, age, gender, medication-use and lifestyle.
Gorjao, R., Verlengia, R., Lima, T. M., Soriano, F. G., Boaventura, M. F., Kanunfre, C. C., Peres, C. M., Sampaio, S. C., Otton, R., Folador, A., Martins, E. F., Curi, T. C., Portiolli, E. P., Newsholme, P., and Curi, R. Effect of docosahexaenoic acid-rich fish oil supplementation on human leukocyte function. Clin Nutr 2006;25(6):923-938. View abstract.
The Federal Government’s Dietary Guidelines for Americans 2015–2020 recommends that adults eat 8 or more ounces of a variety of seafood (fish or shellfish) per week for the total package of nutrients seafood provides, and that some seafood choices with higher amounts of EPA and DHA be included. Smaller amounts of seafood are recommended for young children.

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.