This chapter is a brief introduction to adiabatic quantum computation and quantum annealing, which are analogue forms of quantum computing currently more suited to optimization than standard gate-based quantum computing. The main concepts behind these novel approaches are explained, especially the way in which a discrete hard optimization problem is translated into an equivalent spin glass or QUBO form in order to be solved on a quantum annealing machine, the only type that exists physically at the present time and is commercially available. The present limitations and possible future developments of quantum annealing machines are also briefly discussed, pointing out that there is still room for improvement depending on expected advances in quantum technology.