The dielectric properties of thin-film ferroelectric structures are studied. The effects of compensation charges at the interfaces between layers (e.g. between a ferroelectric and a non-ferroelectric layer) are considered; on the assumption that these charges are mobile within the interface region, we show that they control the domain boundaries between regions of opposite ferroelectric polarization and are thus responsible for the way in which polarization switching takes place. Using a Landau-Devonshire model for the ferroelectric, we demonstrate hysteresis curves (stored charge against applied voltage) in ferroelectric capacitor structures that explain the long-standing problem of why the switching of polarization occurs over a finite voltage range. In particular, the model shows how non-switching ferroelectric layers can be stabilized in thin-film capacitor structures, and why this produces hysteresis curves of the form that is observed experimentally.