Quantum optimization has emerged at the intersection of quantum computing and operations research, driven by the prospect of addressing challenging combinatorial optimization problems through quantum and quantum-inspired computational approaches. This paper provides a structured review of the field from a past, present, and future perspective. We first trace the evolution of quantum optimization from the early development of quantum annealing and quantum adiabatic approaches to the emergence of gate-based quantum algorithms and quantum-inspired optimization methods. We then examine the current state of the field, focusing on the main algorithmic paradigms, their applications, and the practical challenges that currently limit their effectiveness. Particular attention is devoted to the reformulation of optimization problems, the use of quadratic unconstrained binary models and Ising formulations, embedding and connectivity requirements, noise and limited circuit depth, parameter training, and the computational overhead associated with hybrid quantum-classical workflows. Finally, we discuss the future of quantum optimization and identify research directions that may contribute to its practical development, including decomposition-based hybrid methods, cutting-plane strategies, warm-start techniques, problem-specific quantum circuits, tensor-network approaches, and quantum-inspired dynamical systems. Across these three perspectives, the review emphasizes the importance of evaluating quantum optimization through end-to-end computational workflows rather than isolated algorithmic or hardware metrics. Future progress will depend on the coordinated development of mathematical modelling, optimization algorithms, quantum hardware, and rigorous benchmarking against strong classical methods.
This perspective identifies the conditions under which quantum computing may deliver measurable, practically relevant benefits for operations research.