Recent studies of the bias-stress-driven electrical instability of organic field-effect transistors (OFETs) are reviewed. OFETs are operated under continuous gate and source/drain biases and these bias stresses degrade device performance. The principles underlying this bias instability are discussed, particularly the mechanisms of charge trapping. There are three main charge-trapping sites: the semiconductor, the dielectric, and the semiconductor-dielectric interface. The charge-trapping phenomena in these three regions are analyzed with special attention to the microstructural dependence of bias instability. Finally, possibilities for future research in this field are presented. This critical review aims to enhance our insight into bias-stress-induced charge trapping in OFETs with the aim of minimizing operational instability.