A privacy film may have a light-blocking layer that is interposed between first and second transparent substrates. The light-blocking layer may have a plurality of opaque portions and a plurality of transparent portions. The opaque portions may be shaped to ensure light from the display is directed only to the primary viewer of the display. Each opaque portion of the light-blocking layer may extend along a respective longitudinal axis between the first and second transparent substrates. Privacy films used to cover curved displays may have opaque portions that extend along longitudinal axes that have different angles relative to the transparent substrates. Opaque portions in the edge of the privacy film may have longitudinal axes that are at non-perpendicular angles with respect to the transparent substrates. A privacy film for a curved display may also include a light-redirecting layer such as a prism layer or a liquid crystal layer.