Cloud testing is gaining much attention in both academia and industry as an emerging concept in the field of software testing. Cloud testing implies leveraging the resources of the cloud computing environment to overcome deficiencies of the traditional testing approaches. As a result, testing-as-a-service (TaaS) is introduced as a service model that conducts all testing activities in a fully automated manner using cloud-based resources. Performance testing is a type of software testing that validates the performance characteristics of the application under test (AUT) when subjected to different workloads during its operation. Performance characteristics include throughput, response time, and resource utilization of the AUT under a certain workload. This paper focuses on reviewing the literature related to the provision of performance testing as a service (P-TaaS). In this study, we survey the previous work related to cloud-based performance testing. We show the strengths and weaknesses of the current research. Besides, we compare the P-TaaS with the traditional performance testing methodologies. A detailed discussion of the benefits and challenges of P-TaaS is introduced along with identifying the research gaps and the future directions that can be adopted.