Widely adopted for their scalability and flexibility, modern microservice systems present unique failure diagnosis challenges due to their independent deployment and dynamic interactions. This complexity can lead to cascading failures that negatively impact operational efficiency and user experience. Recognizing the critical role of fault diagnosis in improving the stability and reliability of microservice systems, researchers have conducted extensive studies and achieved a number of significant results. This survey provides an exhaustive review of 98 scientific papers from 2003 to the present, including a thorough examination and elucidation of the fundamental concepts, system architecture, and problem statement. It also includes a qualitative analysis of the dimensions, providing an in-depth discussion of current best practices and future directions, aiming to further its development and application. In addition, this survey compiles publicly available datasets, toolkits, and evaluation metrics to facilitate the selection and validation of techniques for practitioners.