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The bulk-heterojunction blend of an electron donor and an electron acceptor material is the key component in a solution-processed organic photovoltaic device. In the past decades, a p-type conjugated polymer and an n-type fullerene derivative have been the most commonly used electron donor and electron acceptor, respectively. While most advances of the device performance come from the design of new polymer donors, fullerene derivatives have almost been exclusively used as electron acceptors in organic photovoltaics. Recently, nonfullerene acceptor materials, particularly small molecules and oligomers, have emerged as a promising alternative to replace fullerene derivatives. Compared to fullerenes, these new acceptors are generally synthesized from diversified, low-cost routes based on building block materials with extraordinary chemical, thermal, and photostability. The facile functionalization of these molecules affords excellent tunability to their optoelectronic and electrochemical properties. Within the past five years, there have been over 100 nonfullerene acceptor molecules synthesized, and the power conversion efficiency of nonfullerene organic solar cells has increased dramatically, from ∼2% in 2012 to13% in 2017. This review summarizes this progress, aiming to describe the molecular design strategy, to provide insight into the structure-property relationship, and to highlight the challenges the field is facing, with emphasis placed on most recent nonfullerene acceptors that demonstrated top-of-the-line photovoltaic performances. We also provide perspectives from a device point of view, wherein topics including ternary blend device, multijunction device, device stability, active layer morphology, and device physics are discussed.