Fullerene derivatives have been widely used for conventional acceptor materials in organic photovoltaics (OPVs) because of their high electron mobility. However, there are also considerable drawbacks for use in OPVs, such as negligible light absorption in the visible-near-IR regions, less compatibility with donor polymeric materials and high cost for synthesis and purification. Therefore, the investigation of non-fullerene acceptor materials that can potentially replace fullerene derivatives in OPVs is increasingly necessary, which gives rise to the possibility of fabricating all-polymer (polymer/polymer) solar cells that can deliver higher performance and that are potentially cheaper than fullerene-based OPVs. Recently, considerable attention has been paid to donor-acceptor (D-A) block copolymers, because of their promising applications as fullerene alternative materials in all-polymer solar cells. However, the synthesis of D-A block copolymers is still a challenge, and therefore, the establishment of an efficient synthetic method is now essential. This review highlights the recent advances in D-A block copolymers synthesis and their applications in all-polymer solar cells.