The changing balance of forces at the nanoscale offers the opportunity to develop a new generation of spatially reconfigurable nanomembrane metamaterials in which electromagnetic Coulomb, Lorentz and Ampère forces, as well as thermal stimulation and optical signals, can be engaged to dynamically change their optical properties. Individual building blocks of such metamaterials, the metamolecules, and their arrays fabricated on elastic dielectric membranes can be reconfigured to achieve optical modulation at high frequencies, potentially reaching the gigahertz range. Mechanical and optical resonances enhance the magnitude of actuation and optical response within these nanostructures, which can be driven by electric signals of only a few volts or optical signals with power of only a few milliwatts. We envisage switchable, electro-optical, magneto-optical and nonlinear metamaterials that are compact and silicon-nanofabrication-technology compatible with functionalities surpassing those of natural media by orders of magnitude in some key design parameters.