Cold sintering is an unusually low-temperature process that uses a transient transport phase, which is most often liquid, and an applied uniaxial force to assist in densification of a powder compact. By using this approach, many ceramic powders can be transformed to high-density monoliths at temperatures far below the melting point. In this article, we present a summary of cold sintering accomplishments and the current working models that describe the operative mechanisms in the context of other strategies for low-temperature ceramic densification. Current observations in several systems suggest a multiple-stage densification process that bears similarity to models that describe liquid phase sintering. We find that grain growth trends are consistent with classical behavior, but with activation energy values that are lower than observed for thermally driven processes. Densification behavior in these low-temperature systems is rich, and there is much to be investigated regarding mass transport within and across the liquid-solid interfaces that populate these ceramics during densification. Irrespective of mechanisms, these low temperatures create a new opportunity spectrum to design grain boundaries and create new types of nanocomposites among material combinations that previously had incompatible processing windows. Future directions are discussed in terms of both the fundamental science and engineering of cold sintering.