The reliance on multi/many-core systems to satisfy the high performance requirement of complex embedded software applications is increasing. This necessitates the need to realize efficient mapping methodologies for such complex computing platforms. This paper provides an extensive survey and categorization of state-of-the-art mapping methodologies and highlights the emerging trends for multi/many-core systems. The methodologies aim at optimizing system's resource usage, performance, power consumption, temperature distribution and reliability for varying application models. The methodologies perform design-time and run-time optimization for static and dynamic workload scenarios, respectively. These optimizations are necessary to fulfill the end-user demands. Comparison of the methodologies based on their optimization aim has been provided. The trend followed by the methodologies and open research challenges have also been discussed.