The application of quantum physics principles has opened the door to a radically different way of conceiving and performing data computation. While still in its infancy, quantum computation offers the potential to efficiently solve problems that are classically considered intractable, thanks to the inherent parallelism granted by quantum effects like superposition and entanglement. The aim of this review is to discuss the potential applications of quantum computation in air transport problems by introducing its main concepts, in addition to how quantum algorithms are designed and their limitations, and then discussing solutions that have already been proposed in the literature. Finally, we draw some conclusions about the factors hindering wider application of quantum computation in air transport and sketch what the future may look like.