Multiple mobile robot systems (MRSs) of different heterogeneity degrees, scales, and interaction levels have been deployed in various application domains. Multi-robot task allocation (MRTA) and motion planning (MRMP) are two key enabling research areas for such successful deployments. While significant progress has been made in both areas, recently, multi-robot integrated task and motion planning (MR-TAMP) is gaining attention from both researchers and industrial practitioners. The main objective is to obtain joint, coupled, and informed plans in both task and motion levels simultaneously to meet certain performance measures. Motivated by both theoretical significance and practical needs, this paper provides the community with a comprehensive survey of this emerging field. Firstly, a complete problem formulation is provided. Then a revised method-centric and a novel method-centric taxonomy are proposed. Based on two taxonomies, major MR-TAMP problems and approaches are surveyed and discussed. Finally, new research opportunities and future challenges are addressed. Note to Practitioners-Mobile robots are key physical equipment in both industries and services, i.e., manufacturing, logistics and warehouse automation, transportation, healthcare, search and rescue, construction, surveillance, and planetary exploration. To realize task-oriented objectives with long-term autonomy, coupled, joint, and informed decision-making at both task and motion levels is essential. This paper provides a comprehensive review of integrated task and motion planning for multi-robot systems. It will help industrial practitioners analyze emerging problems, find solutions, make reasonable decisions, and finally, improve the overall system efficiency.