All-polymer solar cells (APSCs) have attracted immense attention owing to their inherent advantages, including high morphological and mechanical stability under light, thermal, and mechanical stress conditions. Among the components of APSCs, n-type polymer acceptors play a crucial role in improving the photovoltaic properties of these systems. In the past few decades, great efforts have been devoted to the design and synthesis of n-type polymer acceptors for developing high-performance APSCs. Among many kinds of n-type polymer acceptor-related systems, Y6-based polymer acceptors (PY-As) have emerged as an important class for APSCs. Herein, we provide a brief overview of the general device structure and working principles of APSCs. Next, we describe the design strategies of PY-As that have contributed to enhancing the power conversion efficiencies of APSCs. Finally, we discuss the relations between chemical structures and photovoltaic performance of PY-As.