A fundamental assumption of quantum statistical mechanics is that closed isolated systems always thermalize under their own dynamics. Progress on the topic of many-body localization (MBL) has challenged this vital assumption, describing a phase where thermalization, and with it, equilibrium thermodynamics, breaks down.

In this talk, I will describe how we can realize such a phase of matter with ultracold fermions in both driven and undriven optical lattices, with a focus on the relevance of realistic experimental platforms. Furthermore, I will describe new results on the observation of a regime exhibiting extremely slow scrambling, even for "infinite-temperature states" in one and two dimensions. Our results demonstrate how controlled quantum simulators can explore fundamental questions about quantum statistical mechanics in genuinely novel regimes, often not accessible to state-of-the-art classical computations.