Physical processes can inspire the design of algorithms and (meta)heuristics. In recent years, a number of such algorithms, implemented on both quantum and classical computers, have been developed and applied. In this chapter, we provide an outline of the range of these algorithms, focusing on those inspired by quantum physics, and describe some applications, particularly to problems in the domain of operational research. The chapter begins with an overview of the most relevant concepts from physics, including digital quantum computing, annealing, and spin glasses. We give a high-level overview of the current state of quantum computing, including hardware, and discuss its potential and current limitations. The simulated annealing algorithm, as well as the related simulated quantum annealing algorithm, is introduced. The chapter concludes with evolutionary and swarm-based algorithms that derive inspiration from quantum mechanics. Because of the enormous scope of work done in quantum-inspired algorithms and quantum computing, the chapter is necessarily selective in the material covered.