Beyond effectiveness, the robustness of an information retrieval (IR) system is increasingly attracting attention. When deployed, a critical technology such as IR should not only deliver strong performance on average but also have the ability to handle a variety of exceptional situations. In recent years, research into the robustness of IR has seen significant growth, with numerous researchers offering extensive analyses and proposing myriad strategies to address robustness challenges. In this tutorial, we first provide background information covering the basics and a taxonomy of robustness in IR. Then, we examine adversarial robustness and out-of-distribution (OOD) robustness within IR-specific contexts, extensively reviewing recent progress in methods to enhance robustness. The tutorial concludes with a discussion on the robustness of IR in the context of large language models (LLMs), highlighting ongoing challenges and promising directions for future research. This tutorial aims to generate broader attention to robustness issues in IR, facilitate an understanding of the relevant literature, and lower the barrier to entry for interested researchers and practitioners.