Polymeric semiconductors have demonstrated great potential in the mass production of low-cost, lightweight, flexible, and stretchable electronic devices, making them very attractive for commercial applications. Over the past three decades, remarkable progress has been made in donor-acceptor (D-A) polymer-based field-effect transistors, with their charge-carrier mobility exceeding 10 cm 2 V −1 s −1 . Numerous molecular designs of D-A polymers have emerged and evolved along with progress in understanding the charge transport physics behind their high mobility. In this review, the current understanding of charge transport in polymeric semiconductors is covered along with significant features observed in high-mobility D-A polymers, with a particular focus on polymeric microstructures. Subsequently, emerging molecular designs with further prospective improvements in charge-carrier mobility are described. Moreover, the current issues and outlook for future generations of polymeric semiconductors are discussed.