Growing robots apically extend through material eversion or deposition at their tip. This endows them with unique capabilities such as follow the leader navigation, long-reach, inherent compliance, and large force delivery bandwidth. Tip-growing robots can therefore conform to sensitive, intricate, and difficult-to-access environments. This review paper categorizes, compares, and critically evaluates state-of-the-art growing robots with emphasis on their designs, fabrication processes, actuation and steering mechanisms, mechanics models, controllers, and applications. Finally, the paper discusses the main challenges that the research area still faces and proposes future directions.