The advent of quantum computing processors with the possibility to scale beyond experimental capacities magnifies the importance of studying their applications. Combinatorial optimization problems can be one of the promising applications of these new devices. These problems are recurrent in industrial applications and they are in general difficult for classical computing hardware. In this work, we provide a survey of the approaches to solving different types of combinatorial optimization problems, in particular quadratic unconstrained binary optimization (QUBO) problems on a gate model quantum computer. We focus mainly on four different approaches including digitizing adiabatic quantum computing, global quantum optimization algorithms, quantum algorithms that approximate the ground state of a general QUBO problem, and quantum sampling. We also discuss the quantum algorithms that are custom designed to solve certain types of QUBO problems.