Hydrostatic pressure (HP), increasing by 1 atm per 10 m in the ocean, perturbs many cellular processes, for example, by rigidifying membranes and disturbing protein folding and ligand binding. Membranes can be fluidized to work under high HP by increasing unsaturated fatty acids, for example, docosahexaenoic acid. Over generations, some deep‐sea proteins have evolved intrinsic resistance to HP, but often incompletely. These may be protected from HP with piezolytes, small organic molecules with pressure‐counteracting properties. The key example is the osmolyte trimethylamine N‐oxide (TMAO), which marine fishes and crustaceans accumulates linearly with depth. TMAO can effectively counteract many inhibitory effects of HP on numerous proteins. For short‐term HP stress, cellular stress (transient) and homeostasis (persistent) responses (CSRs, CHRs) remain poorly characterized, but across different taxa of shallow and terrestrial organisms, they include common CSR/CHR mechanisms known for other stressors—heat shock proteins (HSPs), boosted energy metabolism, antioxidants, cellular repair systems. For vertically migrating marine animals, HP stress responses are even more poorly characterized. Some species (e.g., Anguilla silver eel, king crab Lithodes maja, snubnosed eel Simenchelys parasiticus) cope with HP changes in their habitat range by intrinsic adaptations, lipid desaturase activation, and metabolic adjustments, but perhaps not common CSR mechanisms. Such species may have constitutive stress proteins and/or are able to adjust membrane saturation and/or TMAO rapidly with depth. For permanent deep‐sea species, CSR/CHR mechanisms have not been directly tested, but evidence in Mariana Trench amphipods and snailfish suggest that HSP and desaturase genes, and possibly piezolyte synthesis, have undergone habitat‐related selection.