Coded aperture compressive imaging is described for two important imaging modalities: Spectral and Tomographic Imaging. Both capture 3D data cubes with just a few 2D detector array measurements. Compressive sensing is then used to reconstruct the 3D information of interest from a set of underdetermined measurements. Notably, the coded apertures used int he measurements play a key role in such imaging systems. This talk will describe the underlying imaging architectures and the intimate link between the coded apertures used and the fundamental principles used in compressive sensing.