Operational instability of organic field-effect transistors (OFETs) is one of the most critical obstacles to their practical use and commercialization. Prolonged operation of OFETs under an applied bias can cause a significant drop in the channel current and a continuous shift in the threshold voltage, which prohibit the normal operation of an electronic device. The bias-stress-driven electrical instabilities are attributed to charge carrier trapping inside the device. In this talk I will discuss the challenges and our progresses in understanding of charge trapping phenomena in OFETs. First, I will briefly introduce the charge trapping phenomenon and discuss how to improve it under using of polymer gate dielectrics. Effects of material characteristics of gate-dielectric polymers on the OFET operation will be focused. Next, I will introduce several approaches for analyzing charge traps at the semiconductor-dielectric interface. The latter part includes our recent studies using photoexcited charge collection spectroscopy, a novel experimental method to probe charge traps. The new spectroscopic method has been applied to investigate the relationships between charge traps and the chemical/physical structure of materials. Especially, I will overview the recently reported polymer semiconductors with high charge mobility yet low crystalline ordering, and present our recent results on bias-stress induced charge trapping for this type of polymer semiconductors. All these systematic study results on the bias instability of OFETs would contribute to unveiling the charge trapping mechanisms and to realizing the robust and practical OFETs eventually.