The tutorial provides an in-depth overview of recent advances in algorithms and data structures for processing graph database queries. The focus will be on scalable algorithms that have been demonstrated to work over real world knowledge graphs. We will also present detailed performance comparisons of classical and recent algorithms. The tutorial will be divided into four sections. The first section will motivate the use of graph databases for querying knowledge graphs, and will introduce the attendees to graph data models and the query language landscape. The second section will discuss how to efficiently evaluate graph patterns, introducing the worst-case optimal join techniques and comparing them to classical join algorithms. The third section will discuss techniques for efficiently evaluating path queries and for constructing compact representations of potentially exponential sets of paths. In the final section we will introduce recent advances in compressed data structures that ease the high memory requirements of worst-case optimal join algorithms and also provide a template for evaluating path queries in a highly optimised manner.