Recent years have seen game semantics emerge as a robust semantic paradigm. It has been used to construct the first fully abstract models for a wide spectrum of programming languages, previously out of reach of denotational semantics. Game semantics models computation as an exchange of moves between two players, representing respectively the program and its computational environment. Accordingly, a program is interpreted as a strategy in a game corresponding to its type. I shall give an overview of the latest developments in the area, which have most recently led to a fully abstract model of Middleweight Java. I will also present a classification of decidable cases for contextual equivalence in a finitary verson of the language, obtained using game semantics and pushdown automata over infinite alphabets. This is joint work with Steven Ramsay and Nikos Tzevelekos.