Metasemantics is a relatively recent philosophical project. Therefore, there are a number of competing approaches to the investigation of the philosophical nature of the study of meaning. In this chapter, I narrow the focus to the foundations of the scientific study of semantics, not the broader philosophical or metaphysical programme often associated with the philosophy of language. The philosophical foundations project allows for a priori metaphysical considerations to trump naturalistic inquiry. The metascientific project, on the other hand, investigates the formal apparatus, mathematics, and scientific structures of semantics as a science. I argue for the latter interpretation over the former. After establishing the remit of the investigation, the principle of compositionality and the general methodology of formal model-theoretic semantics is explored. Next, the role of context is explained and used as a tool to establish a continuum from formal semantics through dynamic approaches to computational distributional semantics. This is just one lens through which to appreciate often overlooked commonalities between disparate theories. Lastly, formal semantic machinery is extended in a number of directions, from lexical semantics to the burgeoning field of supersemantics. The formal finds complex compositional structure below the word and the latter applies it to phenomena beyond language.