<p>In recent times, Multi-Robot Systems (MRS) have garnered extensive attention for their versatility and potential to tackle diverse real-world challenges. Among the myriad problems these systems aim to resolve the Multi-Robot Task Allocation (MRTA) stands out due to its pivotal role in optimizing collective robot performance. MRTA focuses on the efficient distribution of tasks among a group of robots, with objectives often centered around minimizing operational time or maximizing efficiency. This paper sheds light on the significant applications of MRTA, categorizing the predominant methodologies into market, behavior, and optimization-based strategies, with a special emphasis on the latter. Delving into optimization-based approaches, we critically review various studies to highlight their strengths and limitations. This examination reveals the innovative strategies that have emerged in the field, underscoring both the achievements and the persisting challenges within MRTA research. By identifying these gaps, we aim to outline potential directions for future inquiry, suggesting pathways for advancements in MRS efficiency and application breadth. Furthermore, this paper presents a statistical analysis to map the evolution of MRTA strategies over recent years, identifying prevalent methods and noting shifts in research focus. Through this analysis, we aim to expose a extensive overview of the state-of-the-art in MRTA, encouraging further exploration and interdisciplinary collaboration. By emphasizing the critical role of optimization techniques in strategic task allocation, this review aspires to propel the field of multi-robot systems towards new frontiers of innovation and applicability.</p>