Charge-exchange spectroscopy in fusion plasmas entails the use of optical transitions that follow electron transfer from a neutral atom into an excited state of an impurity ion. In most applications, the sources of neutral particles are high-energy beams employed either for heating or for the specific purpose of active plasma diagnosis. The transitions following charge exchange are particularly useful for determining the densities of fully stripped low-Z ions and for measuring ion temperatures and plasma rotation, although they have also been exploited for other purposes. In this review, the atomic physics considerations for interpreting the data, including the influence of the plasma environment, are reviewed, and examples of recent applications to fusion studies are presented.