An implantable ophthalmic device with flexible, fluid-filled membranes provide dynamically variable optical power to restore lost accommodation in individuals suffering from presbyopia or aphakia without moving parts or reducing the amount of transmitted light. Actuating the device causes the fluid-filled membrane to change curvature, which produces a corresponding change in optical power. For instance, squeezing the edge of the membrane causes the center of the membrane to bulge by an amount proportional to the squeezing force. Alternatively, heating or applying a voltage to the membrane may cause the liquid in the membrane to undergo a phase transition accompanied by a corresponding change in volume that causes the membrane to inflate so as to change the optical power of the device.