Spatial data (e.g., points) have extensive applications in practice, such as spatial databases, Location-Based Services, spatial computing, social analyses, computational geometry, graph design, medical imaging, etc. Geometric queries, such as geometric range queries (i.e., finding points inside a geometric range) and nearest neighbor queries (i.e., finding the closest point to a given point), are fundamental primitives to analyze and retrieve information over spatial data. For example, a medical researcher can query a spatial dataset to collect information about patients in a certain geometric area to predict whether there will be a dangerous outbreak of a particular disease (e.g., Ebola or Zika). With the dramatic increase on the scale and size of data, many companies and organizations are outsourcing significant amounts of data, including significant amounts of spatial data, to public cloud data services in order to minimize data storage and query processing costs. For instance, major companies and organizations, such as Yelp, Foursquare and NASA, are using Amazon Web Services as their public cloud data services, which can save billions of dollars per year for those companies and organizations. However, due to the existence of attackers (e.g., a curious administrator or a hacker) on remote servers, users are worried about the leakage of their private data while storing and querying those data on public clouds. Searchable Encryption (SE) is an innovative technique to protect the data privacy of users on public clouds without losing search functionalities on the server side. Specifically, a user can encrypt its data with SE before outsourcing data to a public server, and this public server is able to search encrypted data without decryption. Many SE schemes have been proposed to support simple queries, such as keyword search. Unfortunately, how to efficiently and securely support geometric queries over encrypted spatial data remains open. In this dissertation, to protect the privacy of spatial data in public clouds while still maintaining search functions without decryption, we propose a set of new SE solutions to support geometric queries, including geometric range queries and nearest neighbor queries, over encrypted spatial data. The major contributions of this dissertation focus on two aspects. First, we enrich search functionalities by designing new solutions to carry out secure fundamental geometric search queries, which were not supported in previous works. Second, we minimize the performance gap between theory and practice by building novel schemes to perform geometric queries with highly efficient search time and updates over large-scale encrypted spatial data. Specifically, we first design a scheme supporting circular range queries (i.e., retrieving points inside a circle) over encrypted spatial data. Instead of directly evaluating compute-then-compare operations, which are inefficient over encrypted data, we use a set of concentric circles to represent a circular range query, and then verify whether a data point is on any of those concentric circles by securely evaluating inner products over encrypted data. Next, to enrich search functionalities, we propose a new scheme, which can support arbitrary geometric range queries, such as circles, triangles and polygons in general, over encrypted spatial data. By leveraging the properties of Bloom filters, we convert a geometric range search problem to a membership testing problem, which can be securely evaluated with inner products. Moving a step forward, we also build another new scheme, which not only supports arbitrary geometric range queries and sub-linear search time but also enables highly efficient updates. Finally, we address the problem of secure nearest neighbor search on encrypted large-scale datasets. Specifically, we modify the algorithm of nearest neighbor search in advanced tree structures (e.g., R-trees) by simplifying operations, where evaluating comparisons alone on encrypted data is sufficient to efficiently and correctly find nearest neighbors over datasets with millions of tuples.