Thermalization is the process by which a physical system evolves toward a state of maximal entropy, as permitted by conservation laws. I will begin by outlining the framework used to understand this phenomenon in quantum systems with unitary evolution (Eigenstate Thermalization Hypothesis). Next, I will discuss factors that can hinder or slow down thermalization. One example is long-lived prethermalization, where certain effective (or pseudo-conserved) quantities significantly delay thermalization depending on specific model parameters. This theory is particularly relevant for periodically driven systems, which can exhibit remarkable resistance to heating over extended timescales. I will then explore the possibility of systems that robustly fail to thermalize. Here, robustness refers to the fact that no fine-tuning is required, in contrast with integrable models. Many-body localization (MBL) is the most well-known, and possibly the only example of systems that fail to thermalize on their own. I will examine MBL from both theoretical and numerical perspectives, covering its description in terms of local integrals of motion, the destabilizing effect of quantum avalanches, and recent mathematical advancements. These later developments are welcome given the challenges in properly interpreting numerical results in this field.