A Cochrane analysis of 86 studies involving more than 160,000 participants shows that fish oil capsules have little to no effect on cardiovascular mortality in the average adult. An exception applies to people with a high cardiovascular risk and strongly elevated triglycerides, in whom a high dose of purified prescription EPA did show benefit. Lifestyle factors such as blood pressure, cholesterol, and exercise have considerably more influence on heart health than fish oil supplements.
A Cochrane analysis of 86 studies involving more than 160,000 participants gives a fairly clear answer: for the average adult, fish oil capsules do little to nothing for cardiovascular mortality, and the effect on heart disease in general is small at best. The chance that you as an ordinary user will notice a meaningful benefit is therefore limited.
There is one exception worth mentioning: in people with high cardiovascular risk and strongly elevated triglycerides, a study using a high dose of prescription-grade purified EPA did show a clear benefit. However, that is something quite different from the standard fish oil capsule you buy at a pharmacy, and it concerns a select group under medical supervision.
On the question of safety: ordinary supplements are well tolerated, although you may experience a fishy aftertaste or stomach complaints. At very high doses there is a slightly increased risk of atrial fibrillation, which is the reason not to keep raising the dose indefinitely. For most people considering supplements for general heart safety, blood pressure, LDL cholesterol, exercise and not smoking each have considerably more impact than fish oil.
Moderate evidence, 3 source(s); the direction is probable but not firmly established.