Is There a Causal Chain in Buddhism?

Buddhism is very strong on the question of causality and there's a lot of philosophy has been done on this. But at the same time, they think there's something there that we can refer to in terms of, say, who's Anya, me, and what did I do yesterday? The person I am now is very much based on the person I was then. So there is a line of continuity which Buddhism says is a causal chain. When I've actually read about this, it's very confusing and difficult to pin down.