A novel family of superconductors based on BiS2-based superconducting layers were discovered in 2012. In short order, other BiS2-based superconductors with the same or related crystal structures were discovered with superconducting critical temperatures Tc of up to 10K. Many experimental and theoretical studies have been carried out with the goal of establishing the basic properties of these new materials and understanding the underlying mechanism for superconductivity. In this selective review of the literature, we distill the central discoveries from this extensive body of work, and discuss the results from different types of experiments on these materials within the context of theoretical concepts and models.