Polymerization-induced self-assembly (PISA) is an extremely versatile method for the in situ preparation of soft-matter nanoparticles of defined size and morphologies at high concentrations, suitable for large-scale production. Recently, certain PISA-prepared nanoparticles have been shown to exhibit reversible polymorphism ("shape-shifting"), typically between micellar, worm-like, and vesicular phases (order-order transitions), in response to external stimuli including temperature, pH, electrolytes, and chemical modification. This review summarises the literature to date and describes molecular requirements for the design of stimulus-responsive nano-objects. Reversible pH-responsive behavior is rationalised in terms of increased solvation of reversibly ionized groups. Temperature-triggered order-order transitions, conversely, do not rely on inherently thermo-responsive polymers, but are explained based on interfacial LCST or UCST behavior that affects the volume fractions of the core and stabilizer blocks. Irreversible morphology transitions, on the other hand, can result from chemical post-modification of reactive PISA-made particles. Emerging applications and future research directions of this "smart" nanoparticle behavior are reviewed.