Blind compressive sensing (CS) is considered for reconstruction of hyperspectral data imaged by a coded aperture camera. The measurements are manifested as a superposition of the coded wavelength-dependent data, with the ambient three-dimensional hyperspectral datacube mapped to a two-dimensional measurement. The hyperspectral datacube is recovered using a Bayesian implementation of blind CS. Several demonstration experiments are presented, including measurements performed using a coded aperture snapshot spectral imager (CASSI) camera. The proposed approach is capable of efficiently reconstructing large hyperspectral datacubes. Comparisons are made between the proposed algorithm and other techniques employed in compressive sensing, dictionary learning, and matrix factorization. © 2013 Society for Industrial and Applied Mathematics.