G protein-coupled receptors (GPCRs) respond to a chemically diverse plethora of signal transduction molecules. The notion that GPCRs also signal without an external chemical trigger, i.e., in a constitutive or spontaneous manner, resulted in a paradigm shift in the field of GPCR pharmacology. The discovery of constitutive GPCR activity and the fact that GPCR binding and signaling can be strongly affected by a single point mutation drew attention to the evolving area of GPCR pharmacogenomics. For a variety of GPCRs, point mutations have been convincingly linked to human disease. Mutations within conserved motifs, known to be involved in GPCR activation, might explain the properties of some naturally occurring, constitutively active GPCR variants linked to disease. In this review, we provide a brief historical introduction to the concept of constitutive receptor activity and the pharmacogenomic and structural aspects of constitutive receptor activity.