Shannon-Nyquist theorem rules the signal sampling stating that the signal must be sampled at a rate of at least twice the maximum frequency present in the signal to be fully reconstructed. Compressive Sensing (CS) theory affirms that a sparse signal can be efficiently reconstructed by the acquisition of a number of samples far below the minimal one dictated by Nyquist theorem, thus providing a new approach to data acquisition. CS technique is based on the concept of sparsity. The information rate of a continuous 'sparse' signal may be much smaller than suggested by its bandwidth. The benefit of CS is that it permits to design efficient sensing or sampling protocols that capture the useful information content embedded in a sparse signal and compact it into a small amount of data. A basic example of sparsity is constituted by a multidimensional signal with a strong average spatial and/or spectral autocorrelation, and hence a redundant representation. A mathematical representation, usually a linear transform, of the sparse signal exists in which the number of non-zero coefficients is less than the one in the original representation. The sparse representation is not employed during acquisition, but only during image reconstruction, and it enables signal reconstruction provided that the signal measurements have been acquired using random projections. When radiometric and spectroscopic signals are considered, an optical subsystem would be the natural choice for optically computing such random projections.