Microservice System (MSS) is one of the current promising approaches for realizing modular evolving systems for dynamic and complex environments. However, this promising system faces challenges inherent in its distributed nature, such as the increased complexity and uncertainties of the dynamic environment. Self-Adaptive System (SAS) is a promising solution that can mitigate these problems, it is composed of a control loop that monitors MSS, analyzes changes, plans, and adapts the system accordingly. However, self-adaptation in MSS is a recent emerging field and lacks a comprehensive review of primary studies that consider developed approaches and address related issues and challenges. To overcome, we present a review and analysis of (30) primary studies. Our analysis is conducted systematically using a set of dimensions, including adaptation goals, time, level, logic, actions, and responsibility. The findings reveal that nonfunctional adaptation was the main goal of most studies, and the focus is mainly on the microservices instance level. The most used actions were parametric and adaptation was done, mainly, in an autonomic way. Finally, our review highlights current research gaps and potential directions for future work in this field.