G protein coupled receptors have historically been one of the most druggable classes of cellular proteins. The members of this large receptor gene family couple to primary effectors, G proteins, that have built in mechanisms for regeneration and amplification of signaling with each engagement of receptor and ligand, a kinetic event in itself. In recent years GPCRs, have been found to interact with arrestin proteins to initiate signal propagation in the absence of G protein interactions. This pinnacle observation has changed a previously held notion of the linear spectrum of GPCR efficacy and uncovered a new paradigm in GPCR research and drug discovery that relies on multidimensionality of GPCR signaling. Ligands were found that selectively confer activity in one pathway over another, and this phenomenon has been referred to as ‘biased agonism’ or ‘functional selectivity’. While great strides in the understanding of this phenomenon have been made in recent years, two critical questions still dominate the field: How can we rationally design biased GPCR ligands, and ultimately, which physiological responses are due to G protein versus arrestin interactions? This review will discuss the current understanding of some of the key aspects of biased signaling that are related to these questions, including mechanistic insights in the nature of biased signaling and methods for measuring ligand bias, as well as relevant examples of drug discovery applications and medicinal chemistry strategies that highlight the challenges and opportunities in this rapidly evolving field.