In recent years the quadratic unconstrained binary optimization (QUBO) problem has emerged as a unified framework for modeling and solving a wide variety of combinatorial optimization problems. The unexpected versatility of the QUBO model is opening doors to the solution of a diverse array of important and challenging applications. Developments in this evolving area are illustrated by describing its methodology with examples and by reporting substantial computational experience demonstrating the viability and robustness of the latest methods for solving the QUBO model, showing that they obtain solutions to wide-ranging instances of the model that rival or surpass the best solutions obtained by today’s best special-purpose algorithms.