Omega-3s have been studied in various mood disorders, such as postpartum depression, with some promising results. In bipolar disorder (manic depression), the omega-3s may be most effective for the depressed phase rather than the manic phase of the illness. The omega-3s have also been proposed to alleviate or prevent other psychiatric conditions including schizophrenia, borderline personality disorder, obsessive compulsive disorder, and attention deficit disorder. However, there is still not enough evidence to recommend the omega-3s in these conditions.
Wright, S. A., O'Prey, F. M., McHenry, M. T., Leahey, W. J., Devine, A. B., Duffy, E. M., Johnston, D. G., Finch, M. B., Bell, A. L., and McVeigh, G. E. A randomised interventional trial of omega-3-polyunsaturated fatty acids on endothelial function and disease activity in systemic lupus erythematosus. Ann.Rheum.Dis. 2008;67(6):841-848. View abstract.
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.
There’s evidence that points to the mechanism behind the effects of fish oil on body composition, showing that fat burning at rest is increased with 6 grams/day of fish oil supplementation, and additional research suggests that higher omega-3 levels may be helpful for enhancing satiety during weight loss efforts. Other evidence suggests that fat loss may be a side-effect of the reduction in inflammation that fish oil can help with. Any way you look at it, supporting your dietary habits with 4 or more grams of fish oil per day is probably a good idea!
The question is whether the observed cardiovascular benefits often found among fish eaters is due solely to the oils in fish or to some other characteristics of seafood or to still other factors common to those who eat lots of fish, like eating less meat or pursuing a healthier lifestyle over all. Whatever the answer, it does not seem to be fish oil supplements.
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.
The National High Blood Pressure Education Program in the United States has cautioned against inaccurate publicity of fish oil as an effective means of lowering high blood pressure in patients suffering from hypertension. According to its report, fish oil supplements lower blood pressure in a very small way in hypertensive patients. Research conducted at the Channing Laboratory in Boston has revealed that moderate doses of fish oil supplements have little effect on the condition of high blood pressure in normotensive people.
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. 
Evidence suggests that omega−3 fatty acids modestly lower blood pressure (systolic and diastolic) in people with hypertension and in people with normal blood pressure.[25] Some evidence suggests that people with certain circulatory problems, such as varicose veins, may benefit from the consumption of EPA and DHA, which may stimulate blood circulation and increase the breakdown of fibrin, a protein involved in blood clotting and scar formation.[26][27] Omega−3 fatty acids reduce blood triglyceride levels but do not significantly change the level of LDL cholesterol or HDL cholesterol in the blood.[28][29] The American Heart Association position (2011) is that borderline elevated triglycerides, defined as 150–199 mg/dL, can be lowered by 0.5-1.0 grams of EPA and DHA per day; high triglycerides 200–499 mg/dL benefit from 1-2 g/day; and >500 mg/dL be treated under a physician's supervision with 2-4 g/day using a prescription product.[30]
Giacco, R., Cuomo, V., Vessby, B., Uusitupa, M., Hermansen, K., Meyer, B. J., Riccardi, G., and Rivellese, A. A. Fish oil, insulin sensitivity, insulin secretion and glucose tolerance in healthy people: is there any effect of fish oil supplementation in relation to the type of background diet and habitual dietary intake of n-6 and n-3 fatty acids? Nutr.Metab Cardiovasc.Dis. 2007;17(8):572-580. View abstract.
Damage to the kidneys caused the drug cyclosporine. Cyclosporine is a medication that reduces the chance of organ rejection after an organ transplant. Taking fish oil seems to prevent kidney damage in people taking this drug. Fish oil also seems to improve kidney function during the recovery phase following the rejection of a transplanted organ in people taking cyclosporine.