Recently, all-polymer solar cells (all-PSCs) have made significant progress in terms of efficiency and performance. Using Y-series-based small-molecule acceptors, a new range of polymer acceptors for all-PSC has been developed. These synthesized polymer acceptors have a low band gap, broad absorption, and easily tunable energy levels, making them suitable n-type candidates for efficient all-PSCs. In this review, we summarize some molecular design and synthesis strategies used to advance the field of innovative materials and device engineering involving Y-series-based polymer acceptors to achieve a power conversion efficiency greater than 18% in all-PSCs.