Lysosomes are membrane‐enclosed organelles that mediate the intracellular degradation of macromolecules. They play an essential role in calcium regulation and have emerged as key signaling hubs in controlling the nutrient response. Maintaining lysosomal integrity and function is therefore crucial for cellular homeostasis. Different forms of stress can induce lysosomal membrane permeabilization (LMP), resulting in the translocation to the cytoplasm of intralysosomal components, such as cathepsins, inducing lysosomal‐dependent cell death (LDCD). Here, we review recent advances that have furthered our understanding of the molecular mechanisms of LMP and the methods used to detect it. We discuss several endolysosomal damage‐response mechanisms that mediate the repair or elimination of compromised lysosomes and summarize the role of LMP and cathepsins in LDCD and other cell death pathways. Finally, with the emergence of lysosomes as promising therapeutic targets for several human diseases, we review a variety of therapeutic strategies that seek to either destabilize lysosomes or to maintain, enhance or restore lysosomal function.