We demonstrate the growth of defect-free zinc-blende GaAs nanomembranes by molecular beam epitaxy. Our growth studies indicate a strong impact of As-4 re-emission and shadowing in the growth rate of the structures. The highest aspect ratio structures are obtained for pitches around 0.7-1 mu m and a gallium rate of 1 angstrom s(-1). The functionality of the membranes is further illustrated by the growth of quantum heterostructures (such as quantum wells) and the characterization of their optical properties at the nanoscale. This proves the potential of nanoscale membranes for optoelectronic applications.