Epistemology
Epistemology asks what separates knowing something from merely being right about it.[1] The classical answer is that knowledge is justified true belief: you believe it, it's so, and you have good reason. In 1963 Edmund Gettier produced short counterexamples where all three hold and it still isn't knowledge — you infer a true conclusion from a justified belief that happens to be false, and get the right answer by luck. Sixty years of repair work on that definition is a decent snapshot of the field's method.
The older dispute is about sources. Empiricism says knowledge comes from experience; rationalism says some of it comes from reason alone, prior to any experience. Skepticism presses on both by asking what rules out being systematically deceived. This is where epistemology and metaphysics meet: if nothing in experience could distinguish a real external world from a convincing substitute, then realism and idealism are not settled by looking harder.
A separate question is about structure: not where a belief's support comes from, but what shape the support has. Any reason you give rests on another reason, and that regress has to end somehow — in beliefs that need no further support, or in a web whose parts hold each other up. Foundationalism takes the first option and owes an account of what could sit at the bottom; coherentism takes the second and owes an account of why a coherent story has anything to do with the world. The two objections are mirror images, which is why hybrids keep getting proposed.
It also connects downward to method. Deduction preserves truth but adds nothing; induction reaches beyond the evidence and is what science runs on, at the price of never being certain.