In the last years, Multi-Robot Systems (MRS) have experienced considerable recognition due to various possible real-world applications. Multi-Robot Task Allocation (MRTA) is among the most interesting MRS problems. This problem concerns the situation when a set of given tasks must be performed by a team of mobile robots with the intention of optimizing an objective function (e.g., minimizing the mission time). This paper aims to present MRTA applications and categorizes methods into market-based, behavior-based, and optimization-based approaches. The paper focus on the latter and review several works in order to point out their advantages and limitations and to identify possible future research opportunities. Furthermore, a statistical analysis is provided to identify the most used methods and the evolution of the topic over the years.