Förster (or fluorescence) resonance energy transfer amongst semiconductor quantum dots (QDs) is reviewed, with particular interest in biosensing applications. The unique optical properties of QDs provide certain advantages and also specific challenges with regards to sensor design, compared to other FRET systems. The brightness and photostability of QDs make them attractive for highly sensitive sensing and long-term, repetitive imaging applications, respectively, but the overlapping donor and acceptor excitation signals that arise when QDs serve as both the donor and acceptor lead to high background signals from direct excitation of the acceptor. The fundamentals of FRET within a nominally homogeneous QD population as well as energy transfer between two distinct colors of QDs are discussed. Examples of successful sensors are highlighted, as is cascading FRET, which can be used for solar harvesting.