G-protein coupled receptors (GPCRs) are the most important class of current pharmacological targets. However, it is now widely acknowledged that their regulation is more complex than previously thought: the evidence that GPCRs can couple to several effector pathways, and the existence of biased agonists able to activate them differentially, has introduced a new level of complexity in GPCR drug research. Considering bias represents a challenge for the research of new GPCR modulators, because it demands a detailed characterization of compound properties for several effector pathways. Still, biased ligands could provide an opportunity to modulate GPCR function in a finer way and to separate therapeutic from side effects. Nowadays, a variety of agonists for GPCRs have been described, which differ in their ability to promote receptor coupling to different Gprotein families or even subunits, recruit signal transducers such as arrestins, activate a variety of downstream molecular pathways and induce certain phosphorylation signatures or gene expression patterns. In this review, we will cover some of the experimental techniques currently used to understand and characterize biased agonism and discuss their strengths and limitations. Additionally, we will comment on the computational efforts that are being devoted to study ligand-induced bias and on the potential they hold for rationalizing its structural determinants. Finally, we will discuss which of these strategies could be used for the rational design of biased ligands and give some examples of the potential therapeutic value of this class of compounds.