By creating certain marks on paper, or by making certain sounds—breathing past a moving tongue—or by articulation of hands and bodies, language users can give expression to their mental lives. With language we command, assert, query, emote, insult, and inspire. Language has meaning. This fact can be quite mystifying, yet a science of linguistic meaning—semantics—has emerged at the intersection of a variety of disciplines: philosophy, linguistics, computer science, and psychology.  The past fifty years have seen an explosion of research into the semantics of natural languages. There are now sophisticated theories of phenomena that were not even known to exist mere decades ago. Much of the early work in natural language semantics was accompanied by extensive reflection on the aims of semantic theory, and the form a theory must take to meet those aims. But this meta-theoretical reflection has not kept pace with recent theoretical innovations. The purpose of this volume is to re-address these questions concerning the foundations of natural language semantics in light of the current state-of-the-art in semantic theorising.