Continuous improvements have been made to drive the impressive progress of solution-processed bulk-heterojunction polymer solar cells (BHJ PSCs), in which the rationally designed conjugated polymers have played a significant role. Currently, a power conversion efficiency (PCE) of > 12% has been achieved in fullerene-based BHJ PSCs, while non-fullerene-based BHJ PSCs have demonstrated more promising PCEs of > 15% in single-junction cells and > 17% in tandem cells, respectively. In this review, we summarize the important advances of conjugated polymers developed recently for both high-performance fullerene- and non-fullerene-based PSCs, including both p-type and n-type polymers. The associated design strategies of polymer donors in the fullerene-based PSCs will be reviewed first, followed by a discussion of the recent advances in design of polymer acceptors in all-polymer PSCs. The development of complementary polymer donors in the all-polymer PSCs will also be discussed. A brief summary of the recent progress of the state-of-the-art small-molecule NFAs and the advances of their pairing polymer donors will be provided. Finally, a summary and outlook for advancing the device performance and associated stability of BHJ PSCs will be given and new perspectives for future research will be highlighted. We aim to provide the readers with a comprehensive understanding of the roles and functions of conjugated polymers play in this fast-growing field.