In recent years, new metaheuristic algorithms have been developed taking as reference the inspiration on biological and natural phenomena. This nature-inspired approach for algorithm development has been widely used by many researchers in solving optimization problem. These algorithms have been compared with the traditional ones algorithms and have demonstrated to be superior in complex problems. This paper attempts to describe the algorithms based on nature, that are used in fuzzy clustering. We briefly describe the optimization methods, the most cited nature-inspired algorithms published in recent years, authors, networks and relationship of the works, etc. We believe the paper can serve as a basis for analysis of the new are of nature and bio-inspired optimization of fuzzy clustering.