In industry, RESTful APIs are widely used to build modern Cloud Applications. Testing them is challenging, because not only do they rely on network communications, but also they deal with external services like databases. Therefore, there has been a large amount of research sprout in recent years on how to automatically verify this kind of web services. In this article, we present a comprehensive review of the current state-of-the-art in testing RESTful APIs based on the analysis of 92 scientific articles. These articles were gathered by utilizing search queries formulated around the concept of RESTful API testing on seven popular databases. We eliminated irrelevant articles based on our predefined criteria and conducted a snowballing phase to minimize the possibility of missing any relevant paper. This survey categorizes and summarizes the existing scientific work on testing RESTful APIs and discusses the current challenges in the verification of RESTful APIs. This survey clearly shows an increasing interest among researchers in this field, from 2017 onward. However, there are still a lot of open research challenges to overcome.