|Abstract:||Data visualization is the primary means by which data analysts explore patterns, trends, and insights in their data. Despite of their growing popularity, existing visualization tools (e.g., Tableau, PowerBI, Excel) are limited in their ability to automatically find desired visualizations or insights. As a result, the process of visual data exploration is manually-intensive and time-consuming, and becomes simply unsustainable as the complexity and scale of the dataset increases. In this dissertation, we address the shortcomings of existing visualization tools by facilitating expressive and scalable data exploration. In particular, we propose two systems: 1) Zenvisage—for effortlessly and efficiently finding visualizations with specific patterns or insights among large collections, and 2) ShapeSearch—for finding visualizations based on fine grained and fuzzy patterns. Both Zenvisage and ShapeSearch draw heavily from use-cases in a variety of domains including biology, battery science, and cosmology, and provide expressive visual primitives to capture a large variety of data exploration needs. Backed by formal algebra and semantics, the visual primitives help operate on collections of visualizations (e.g., by composing, filtering, comparing, matching, and sorting) based on visual trends and patterns. Furthermore, these systems support built-in recommendations, and multiple flexible query specification mechanisms, including intuitive interactions and natural language, simultaneously catering to the needs of both novice and expert analysts. To automatically parse and execute visual queries efficiently, Zenvisage and ShapeSearch support a suite of optimizations, that can traverse and evaluate a large number of visualizations within interactive response times. We document performance results, as well as results from multiple user- and case-studies that demonstrate that users are able to effectively use Zenvisage and ShapeSearch to eliminate error-prone and tedious exploration and directly identify desired visualizations.