Active deformable sheets are integrated smart planar sheet structures performing off-plane deformations under computer actuation and control, to take up a desired dynamic 3-D morphology specified in CAD software or obtained by 3-D scanning of a solid surface. The sheet prototypes are implemented in the laboratory by elastic neoprene foil layers with embedded asymmetric grids of shape memory alloy (SMA) wires [nickel-titanium Naval Ordinance Laboratory (Nitinol)], which on electrical contraction bend the sheet to the necessary local curvature distribution. An analytical model of such prototypes, consisting of an electrical, thermal, material, and mechanical module, as well as a more complex finite element mechanical simulation of the sheet structure, have been developed and validated experimentally. Besides open-loop control of the sheet curvatures by modulation of the SMA wire actuation current, a closed-loop control system has been implemented, using feedback of the wire electrical resistance measurements in real time, correlating to the material transformation state. Prototypes with a reflective foil surface are also tested as cylindrical reflectors with real-time variable focal length. The active deformable sheets are intended for applications such as reconfigurable airfoils and aerospace structures, optics and electromagnetic reflectors, flexible and rapid tooling, and microrobotics.