We demonstrate two complementary applications based on compressive imaging: hyperspectral compressive structured illumination for three-dimensional imaging and compressive classification of objects using neural networks. The structured light method usually uses structured patterns generated from a commercial digital projector which contain very limited spectral content, using white light or RGB-based giving very little material content and not exploiting possible wavelength-dependent scattering. Therefore we designed and implemented a hyperspectral projector system that is able to generate structured patterns consisting of arbitrarily defined spectrum instead. We used the system to recover the unique spectrum-dependent 3-D volume density of the colored targets of participating media. For the image classification problem, it is known that a set of images of a fixed scene under varying articulation parameters forms a low-dimensional, nonlinear manifold that random projections can stably embed using far fewer measurements. Thus random projections in compressive sampling can be regarded as a dimension-reducing process. We demonstrate a method using compressive measurements of images to train a neural network that has a relatively simple architecture for object classification. As a proof of concept, simulations were performed on infrared vehicle images that demonstrated the utility of this approach over previous compressive matched filtering. The success of both these projects bodes well for their overall integration into a single infrared compressive hyperspectral machine-vision instrument.