Cloud computing has emerged as a promising platform for running scientific workflows across various domains. Scientists can take advantage of different cloud service models, such as serverful or serverless, to execute workflows based on their specific requirements, along with diverse pricing models like on-demand, reserved, or spot instances to reduce execution costs. However, the challenge of selecting appropriate resources and pricing models, coupled with the orchestration and scheduling of workflow tasks, creates significant complexity for users. To mitigate this burden, Workflow as a Service (WaaS) brokers have been introduced to facilitate workflow execution. In recent years, numerous studies have been published, either directly or indirectly related to this research area, highlighting the need for a comprehensive and systematic review of WaaS brokers to identify key trends and challenges in this field. In this paper, we conduct a Systematic Mapping Study (SMS) on WaaS brokers within cloud environments. The SMS employs a thorough 3-tier strategy (database search, backward snowballing, and forward snowballing) to answer five research questions. A total of 87 high-quality articles, published in 49 prestigious venues, are analyzed to derive a taxonomy based on the architecture of WaaS brokers. The articles are classified and surveyed according to this taxonomy, and future research directions for the design and implementation of WaaS brokers are explored. This study provides valuable insights for researchers and developers, helping them identify major trends and issues in the field of WaaS brokers.