This paper is a survey article on mathematical theories and techniques used in the study of swing options. In financial terms, swing options can be regarded as multiple-strike American or Bermudan options with specific constraints on the exerciseability. We focus on two categories of approaches: martingale and Markovian methods. Martingale methods build on purely probabilistic properties of the models whereas Markovian methods draw on the interplay between stochastic control and partial differential equations. We also review other techniques available in the literature.