 Quine and Davidson’s idea that serious philosophy should use only extensional notions faded in the latter half of the twentieth century, which witnessed an intensional revolution: a collective effort to analyze notions which are fundamental for our understanding of the world and of ourselves, like belief, information, knowledge, meaning, content, essence, explanation, via a single theoretical system: employing possible worlds and constructions out of them. Standard possible worlds semantics (SPWS) found applications in logic, linguistics, game theory, artificial intelligence: a success story of philosophy. However, many of these phenomena (and, more: a survey in  Section 1)  are, arguably, hyperintensional, requiring hyperintensional language to do them justice. And SPWS tends to collapse any distinctions more fine-grained than necessary equivalence. The issue of how best to address hyperintensionality has emerged in piecemeal fashion, via a series of difficulties of SPWS (in  Section 1,  we list a few). Some have denied that hyperintensionality marks a set of real phenomena and have tried to explain away hyperintensional intuitions. Some of these general attempts are discussed in  Section 2.