Recently, Multi-Robot Systems (MRS) have attained considerable recognition because of their efficiency and applicability in different types of real-life applications. This paper provides a comprehensive research study on MRS coordination, starting with the basic terminology, categorization, application domains, and finally, give a summary and insights on the proposed coordination approaches for each application domain. We have done an extensive study on recent contributions in this research area in order to identify the strengths, limitations, and open research issues, and also highlighted the scope for future research. Further, we have examined a series of MRS state-of-the-art parameters that affect MRS coordination and, thus, the efficiency of MRS, like communication mechanism, planning strategy, control architecture, scalability, and decision-making. We have proposed a new taxonomy to classify various coordination approaches of MRS based on the six broad dimensions. We have also analyzed that how coordination can be achieved and improved in two fundamental problems, i.e., multi-robot motion planning, and task planning, and in various application domains of MRS such as exploration, object transport, target tracking, etc.