 The quantum speed limit, QSL, is a bound on the minimum time required for a quantum system to evolve between two states, but there is no simple relationship between memory effects and the tightness of this bound for open quantum systems. Only specific classes of dynamical evolutions and initial states have a link between non-Markovianity and the QSL, shedding light on the connection between information backflow between system and environment and the speed of quantum evolution. This article was authored by J. Titanen, H. Lyra, and S. Maniscalco.