In the past few years, tremendous progress in power conversion efficiency (PCE) of polymer solar cell (PSC) via design of novel conjugated polymers has been made. In order to further promote PCE, an efficient way is to narrow down optical band gap of the polymers. This review focuses on low band gap polymers based on Donor—Acceptor (D—A) strategy and quinoid form structure. At first, we introduce the requirements for polymers, such as tuning of energy levels. Second, we introduce the importance of main chain, side chain and substituents, which affect the optical and electrical properties, intra/intermolecular interactions, and charge mobility. We survey the important donor and acceptor units and discuss the guidelines for developing highly efficient conjugated polymers. We classify the polymers into several categories in accordance with the structures of acceptor units: Benzodiathiazole (BT), Thienopyrrolodione (TPD) and Diketopyrrolopyrrole (DPP), to which the copolymers with various donors have promissing efficiency. Low band gap polymers based on the quinoid structure, thienothiophene (TT), having promising efficiency are also included.