Earth-abundant and environmentally benign antimony selenide (Sb2Se3) has emerged as a promising light-harvesting absorber for thin-film photovoltaic (PV) devices due to its high absorption coefficient, nearly ideal bandgap for PV applications, excellent long-term stability, and intrinsically benign boundaries if properly aligned on the substrate. The record power conversion efficiency of Sb2Se3 solar cells has currently reached 9.2%, however, it is far lower than the champion efficiencies of other chalcogenide thin-film solar cells such as CdTe (22.1%) and Cu(In,Ga)Se2 (23.35%). The inferior device performance of Sb2Se3 thin-film solar cells mainly results from a large open-circuit voltage deficit, which is strongly related to the interface recombination loss. Accordingly, constructing proper band alignments between Sb2Se3 and neighboring charge extraction layers through interface engineering to reduce carrier recombination losses is one of the key strategies to achieving high-efficiency Sb2Se3 solar cells. In this review, the fundamental properties of Sb2Se3 thin films, and the recent progress made in Sb2Se3 solar cells are outlined, with a special emphasis on the optimization of energy band alignments through the applications of electron-transporting layers and hole-transporting layers. Furthermore, the potential research directions to overcome the bottlenecks of Sb2Se3 thin-film solar cell performance are also presented.