The processes by which agonist binding promotes biological activity is a key issue in G protein-coupled receptor (GPCR) pharmacology, with much of our understanding governed by the application of mathematical models to experimental data. Models are built upon decades of fundamental principles, providing key concepts and measurable parameters which quantify agonism. Whilst numerous general receptor activation models exist, such as the operational model of agonism, there is no single model capable of describing all functional effects. Instead, there are a variety of models, each employed to understand specific experimental observations. In this review, we summarise recent GPCR models which incorporate: multiple signalling pathways simultaneously, constitutive receptor activity, or receptor dynamics, whilst providing parameters to quantify agonist bias. We also describe how model parameterisation requires model organisms and advanced experimental techniques, both proving invaluable for the construction of more complex, mechanistic models.