Current hyperspectral imaging and video is limited due to optical hardware as well as challenges in the sheer amount of data that needs to be acquired. Compressive sensing presents a viable alternative for simplifying hardware and allows for the subsampling of the high-dimensional datacube, but is limited by long L1 reconstruction times. Therefore, here we demonstrate new approaches in reducing the time required to acquire and reconstruct the data for compressive hyperspectral images and video in multiplexing cameras. In the first method, we develop and utilize a procedure to reduce the reconstruction time in spatially-multiplexing single-pixel cameras using compressive foveation, Setting it apart from previous single-pixel foveation procedures is that our method actually allows for the selection of a region of interest after all measurements have been acquired and without any need for adaptive sensing. In addition, we provide a proof-of-concept method of hyperspectral microscopy based in spectral multiplexing that is capable of capturing hyperspectral images of the sample in a matter of seconds with over 100 bands while maintaining a megapixel spatial resolution. Both results presented represent significant advances in compressive hyperspectral imaging.