G-protein coupled receptors (GPCRs) are the largest family of membrane proteins engaged in transducing signals from the extracellular environment into the cell. GPCR-biased signaling occurs when two different ligands, sharing the same binding site, induce distinct signaling pathways. This selective signaling offers significant potential for the design of safer and more effective drugs. Although its molecular mechanism remains elusive, big efforts are made to try to explain this mechanism using a wide range of methods. Recent advances in computational techniques and AI technology have introduced a variety of simulations and machine learning tools that facilitate the modeling of GPCR signal transmission and the analysis of ligand-induced biased signaling. In this review, we present the current state of in silico approaches to elucidate the structural mechanism of GPCR-biased signaling. This includes molecular dynamics simulations that capture the main interactions causing the bias. We also highlight the major contributions and impacts of transmembrane domains, loops, and mutations in mediating biased signaling. Moreover, we discuss the impact of machine learning models on bias prediction and diffusion-based generative AI to design biased ligands. Ultimately, this review addresses the future directions for studying the biased signaling problem through AI approaches.