Hyperspectral imaging is a challenging task given the high dimensionality of data and the limitations of conventional sensing scheme and detector design. Yet, it has great potential in studying optical phenomena in both science and engineering, and in both microscopic and macroscopic systems. Simultaneously, machine vision is an important field with a wide range of real-world applications. There has been constant effort to improve the accuracy and efficiency of machine vision implementations. The field of compressive sensing and its ability to exploit the inherent sparsity of a majority of natural images have the potential to make a tremendous impact on both of these fields. As such, the first part of this thesis describes the design and implementation of a compressive hyperspectral microscope that can capture and analyze different properties of metallic nanoparticles, fluorescent microspheres and two-dimensional materials. In relation to macroscale imaging, a hyperspectral projector system is developed and implemented as discussed in the middle portion of this thesis. It enhances conventional structured illumination methods by incorporating hyperspectral compressive measurements. Lastly, a general and efficient dynamic-rate training scheme for neural networks is developed and implemented that specifically exploits compressive measurements. The approach is capable of performing classification over a range of measurement rates directly on compressive measurements acquired by a single-pixel camera architecture bypassing image reconstruction. Since the input layer of the network is designed to couple with a single sensor, this approach is also compatible with a compressive hyperspectral imager. Overall, the results in this thesis presents many novel ways in which compressive sensing can greatly benefit both hyperspectral imaging and machine vision tasks.