The science of optical remote sensing includes aerial, satellite, and spacecraft observations of scenes or targets. Various diverse sensing modalities are useful, and a variety of types of on-board sensors are employed for data collection. The optical sensing modalities we are concerned with are Hyperspectral (HSI) imaging and Light Detection and Ranging (LiDAR). HSI sensing collects information across a wide range of the electromagnetic spectrum while LiDAR is a remote sensing technology that collects RGB data while measuring distance by illuminating a target area with lasers and analyzing the reflected light. Fusion and resulting interrogation of multi-modal (HSI and LiDAR) images is an extremely important, but challenging, aspect of geospatial imaging. In this talk we briefly discuss some recent mathematical techniques for HSI and LiDAR data fusion, geometric feature and pattern representation, for dimensionality reduction, classification, target detection and identification. Illustrations of the algorithms are provided on both simulated and real data. We then concentrate on recent work involving wavelength dependent hyperspectral PSF estimation and associated joint deblurring and sparse unmixing using Alternating Direction Method of Multipliers (ADMM) optimization for convex inverse problems. Joint work with Dejan Nikic and Jason Wu (Boeing); and Paul Pauca, Todd Torgersen and Peter Zhang (Wake Forest), Sebastian Berisha and James Nagy (Emory) and others to be listed in the presentation.