In the classical thermal Mpemba effect, an initially hot system relaxes faster to the final equilibrium state than a cold one. Quantum generalizations of this effect - described already by Aristotle - are of topical interest as they allow for speeding up quantum tasks like state preparation or manipulation. In this talk, I describe the generalization of the classical theory to the case of open Markovian quantum systems coupled to multiple (fermionic or bosonic) reservoirs. We obtain a classification of possible quantum Mpemba effects in open quantum systems. I will illustrate quantum Mpemba effects for a generic open two-level system, and for an interacting two-site (“poor man”) Kitaev model and an Anderson impurity coupled to two metallic leads. In all these cases, the quantum system of interest is coupled to several reservoirs and can be operated under nonequilibrium steady-state conditions.