A review of fundamental and practical limitations on ferroelectric thin-film non-volatile random access memories is given. Size effects are considered (both thickness and lateral dimensions) from the point of view of both depolarization field instabilities and electrical breakdown mechanisms. Emphasis is on switched-capacitor pass-gate architectures, but true ferroelectric FETs (in which the metal gate in the field-effect transistor is replaced with a ferroelectric film) are discussed briefly. The conclusion is that ferroelectric non-volatile RAMs of Gigabit densities are technically viable in the immediate future.