Late 20th early 21st century philosophy

Well, since then, but also then, there is analytic philosophy, which is (in various forms) still the dominant view in the English speaking countries. I don' t think there are any prominent Existentialists. Maybe on the Continent, but all kinds or weird things go on there anyway. The late W.V. Quine is still very influential, and so are Saul Kripke, Daniel Dennett, and others (of course). I think that if you were to begin to read Quine and others, you would have to retool yourself. And certainly become familiar with some technical logic.

It's hard to say what's happened in philosophy since the 1970s since something new is being done always and everywhere. What you characterise as most important, and even what work one is aware of, is going to be determined by your own interests to a certain extent.

A few recent books that are particularly interesting and of unquestionable importantance:
Naming and Necessity (1980) Kripke - Attacks the descriptive theory of names, and puts forward a causal theory in its place (to put it simply, Kripke's positive solution is a bit more subtle).

Wittgenstein on Rules and Private Language (1982) Kripke - An interpretation of Wittgenstein's thoughts on rule following which has been very important in the development of meaning scepticism and the social aspect of meaning.

Mind and World (1994) McDowell - A difficult and complex book which makes it hardto summarise. In a nutshell, he argues that we can only make sense of thought being directed at an objective world (intentionality) if we adopt a minimal empiricism, and that this is only tenable if we view experience as being conceptually structured and construed as an "openness to the layout of reality".

The View From Nowhere (1986) Nagel - I've only read bits of this, but it deals with the "objective point of view", the human ability to "take a step back" and view things from a detached viewpoint, and how it comes in to a wide range of philosophical problems.

Subjective, Intersubjective, Objective (2001) Davidson - Davidson has been another hugely important philosopher since the 1970s (and before), but he has only published in essays. This collection largely deals with the emergence of rationality, thought and language, and contains some of my favourite later Davidson essays. Highlights include 'A coherence theory of truth and knowledge', 'The Myth of the Subjective', 'The Emergence of Thought', 'Rational Animals' and 'Three Varieties of Knowledge'.