Quantum computing is a new computing paradigm that has been advocated to be transformative for hard combinatorial optimization. The real picture is however more nuanced, having some quantum-based algorithms offering new heuristics to well-established problems. In this talk, I will give you a tour d’horizon in variational algorithms on quantum computers for combinatorial problems. I will point out challenges, opportunities, and the hope we have in make quantum optimization useful. In particular, I will present some initial results in quadratic assignment problems and permutation-based problems in general.