Modern web services routinely provide REST APIs for clients to access their functionality. These APIs present unique challenges and opportunities for automated testing, driving the recent development of many techniques and tools that generate test cases for API endpoints using various strategies. Understanding how these techniques compare to one another is difficult, as they have been evaluated on different benchmarks and using different metrics. To fill this gap, we performed an empirical study aimed to understand the landscape in automated testing of REST APIs and guide future research in this area. We first identified, through a systematic selection process, a set of 10 state-of-the-art REST API testing tools that included tools developed by both researchers and practitioners. We then applied these tools to a benchmark of 20 real-world open-source RESTful services and analyzed their performance in terms of code coverage achieved and unique failures triggered. This analysis allowed us to identify strengths, weaknesses, and limitations of the tools considered and of their underlying strategies, as well as implications of our findings for future research in this area.