Generally, service interactions in dynamic environments comprising cloud computing, Internet of Things (IoT), and etc. occur in an unspecified situation causing trust management a significant aspect. The widespread usage of services in today's vastly high-tech world reveals the rising necessity of trust management in terms of services. In dynamic environments, there are not enough confidences for users to recognize trustworthy service providers. Hence, evaluating and managing the trustworthiness of services is a vital challenge for enabling customers to select trustworthy resources in dynamic environments. To the extent of our knowledge, in spite of the vital role of Trust Management of Services (TMoS), there is not any thorough and systematic work in this scope with a specific focus on services. Thus, this research investigates the current methods of trust management in terms of services, which are published up to February 2020. We have identified 68 papers that are diminished to 22 mostly qualified papers through the article selection process. Also, we have examined and compared the selected papers in terms of their merits and demerits, considering the important parameters in this field. The investigation results point out that the security, scalability, and dynamicity are essential to almost all research. Furthermore, privacy and reliability are the most essential parameters in the field of TMoS. Moreover, the statistical results and information can contribute to future works; also, we have conducted some open issues and future work suggestions that could be an effective roadmap for future researchers in this area.