The primary function of a database system is to efficiently compute correct answers to user queries. Therefore, robust query processing (RQP), where strong numerical guarantees are provided on query performance, has been a long-standing core objective in the design of industrial-strength database engines. Unfortunately, however, RQP has proved to be a largely intractable and elusive challenge, despite sustained efforts spanning several decades. In this monograph, a holistic coverage of the RQP innovations is provided, and strengths and limitations are highlighted. Further, open technical problems that remain to be solved to make RQP a contemporary reality are also enumerated.In this monograph, representative techniques along these various dimensions are covered. After the introduction, a background to RQP is given. In the chapters thereafter, the authors cover Robust Operators, Plans, and Execution, and then Structural Bounds, Cost Models and Machine Learning Techniques are surveyed. The monograph concludes with a chapter on Holistic Robustness, and Future Directions.The target audience for this monograph includes researchers, developers and students with an interest in the internals of database engines.