We describe a high-throughput hyperspectral microscope. The system replaces the slit of conventional pushbroom spectral imagers with a static coded aperture mask. We present the theoretical underpinnings of the aperture coded spectral engine and describe two proof-of-concept experimental implementations. Compared to a conventional pushbroom system, the aperture coded systems have 32 times greater throughput. Both systems have about a 1 nm spectral resolution over the spectral range of 550-665 nm. For the first design, the spatial resolution for the system is 5.4 microm while the spatial resolution for the second system ranges from 7.7 microm to 1.54 microm. We describe experimental results from proof-of-concept applications of the imager to hyperspectral microscopy.