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Non-expert summaryThis is a review of the fluid mechanics associated with blistering, which occurs when a thin solid layer locally separates from an underlying substrate through cracking of a bulk material, delamination of a composite material, or peeling of a thin layer (membrane) adhered to the substrate by a thin layer of viscous fluid. The focus of the review is on the latter case, where the expansion of the newly formed blister by fluid injection occurs via a displacement flow, which peels the adhered surfaces apart through a two-way interaction between flow and deformation. These blisters are prone to fluid- and solid-mechanical instabilities. If the injected fluid is less viscous than the fluid already occupying the gap, patterns of short and stubby fingers (fingering) form on the propagating fluid interface. Buckling/wrinkling instabilities of the delaminated layer can arise for sufficiently thin membranes and can interact with the fluid mechanical fingering instability.