Organic solar cells (OSCs) have attracted lots of research attention and significant developments have been achieved in the last decade. Small molecular acceptors (SMAs) have played an important role. During the last five years, non-fullerene small molecular acceptors (NFSMAs) have replaced fullerene ones and become the research focus of OSCs, due to their excellent optoelectronic properties, such as wide and strong absorption, easily adjustable energy levels and stable morphology. This review highlights the recent advances of SMAs, especially NFSMAs including perylenediimide, naphthalenediimide, diketopyrrolopyrrole, indacenodothiophene, and Y6 series. The relationships among molecular structures, optical properties, energy levels, device processing methods and photovoltaic performance are systematically analyzed and summarized. Challenges, strategies and prospects are also discussed. This review may provide new guidances for designing high-performance SMAs.