Logical semantics includes once again structured meanings in its repertoire. The leading idea is that semantic and syntactic structure are more or less isomorphic. A key motive for reintroducing sensitivity to semantic structure is to obtain fine-grained meanings, which are individuated more finely than in possible-world semantics, namely up to necessary equivalence. Just getting the truth-conditions right is deemed insufficient for a full semantic analysis of sentences. This paper surveys some of the most recent contributions to the program of structured meaning, while providing historical background. I suggest that to make substantial advances the program needs to solve the problem of propositional unity and develop an intensional mereology of abstract objects.