Mammalian cells contain numerous membrane-bound organelles, of which endosomes serve as the initial destination for endocytosed molecules. Therapeutic agents are also internalized by cells and transported to endosomes or phagosomes, and subsequently delivered to lysosomes for degradation. Therefore, these agents require drug delivery systems (DDSs) that enable their escape from endosomes into the cytosol before lysosomal degradation; however, endosomal escape is a major limitation of current DDSs. Studies of bacterial phagosomal escape have revealed mechanisms by which host cells detect damage to organelle membranes. These membrane damage-sensing molecules also recognize membrane damage caused by artificial DDSs or physical energy-based insults. In this review, we summarize molecular mechanisms underlying the early stages of membrane damage in the plasma membrane, lysosomes and bacteria-containing vacuoles (BCVs) to better understand the early stages of endosomal membrane damage in the absence of pathogens. We summarize recent advances in galectins, endosomal sorting complexes required for transport (ESCRT) complexes, sphingomyelin, stress granules, phosphatidylinositol 4-phosphate (PI4P) at membrane contact sites, as well as annexins. We also discuss the recruitment kinetics of these molecules to damaged membranes. Although the recruitment kinetics vary depending on cell type and experimental conditions, this information provides a timeframe for the events following membrane damage, including damage sensing, membrane repair, and degradation of damaged organelles. We also discuss a potential fourth event, fusion between the plasma membrane and endosomes or lysosomes for membrane repair in annexin section. Finally, we summarize approaches for inducing “sterile” endosomal membrane damage. Future development of these approaches may facilitate the design of novel DDSs and physical energy-based strategies for manipulating specific organelles.