With the advancement of GPS and remote sensing technologies, an enormous amount of geospatial data are being collected from various domains. Examples include crime locations, road temporally detailed networks, earth observation imagery, and GPS trajectories. Geospatial data science studies computational techniques to discover interesting, previously unknown, but potentially useful patterns from large spatial datasets. It is important for various applications. Crime hotspot detection helps law enforcement departments to create effective strategies to allocate police resources and to prevent crimes. Earth observation imagery classification plays a crucial role in flood extent mapping and water resource management. Big companies like UPS use truck GPS trajectories data to find efficient routes that can ultimately minimize the delivery time and reduce carbon footprint. However, geospatial data science poses several computational challenges. First, the spatial data volume is rapidly growing. For example, NASA collects around 12TB of earth observation imagery per day. Second, spatial data exhibits spatial dependency which imply nearby samples are not statistically independent. Third, different spatial patterns of interest may exist in different spatial scales. Finally, there can be limited observations. For example, sometimes it can be difficult or even impossible to get the complete observation of spatial features in an area due the presence of obstacles (e.g., clouds). My thesis investigates novel geospatial data science techniques to address some of these challenges. I propose novel parallel spatial colocation mining algorithms on GPUs to address the challenge of large data volume. Similarly, I propose a deep learning framework to automatically map the road safety features from streetview imagery that captures spatial dependency. Next, I propose a novel approach to address the challenge of limited observation based on the physics-aware spatial structural constraint. Finally, I propose a novel spatial structured model called hidden Markov contour tree (HMCT), a contour tree structure, to capture directed spatial dependency on flow directions between all locations on a 3D surface.