The rapid growth of Large Language Models (LLMs) presents significant privacy, security, and ethical concerns. While much research has proposed methods for defending LLM systems against misuse by malicious actors, researchers have recently complemented these efforts with an offensive approach that involves red teaming, i.e., proactively attacking LLMs with the purpose of identifying their vulnerabilities. This paper provides a concise and practical overview of the LLM red teaming literature, structured so as to describe a multi-component system end-to-end. To motivate red teaming we survey the initial safety needs of some high-profile LLMs, and then dive into the different components of a red teaming system as well as software packages for implementing them. We cover various attack methods, strategies for attack-success evaluation, metrics for assessing experiment outcomes, as well as a host of other considerations. Our survey will be useful for any reader who wants to rapidly obtain a grasp of the major red teaming concepts for their own use in practical applications.