Efficient regression testing plays an important role for organizations that have large investment in active, ever-changing software development. Efficiency can be obtained by optimizing the test cases as it provides a balance between the safety and precision. Many optimization techniques from various domains have been applied in regression testing for optimizing the search and the solutions. But nature-inspired algorithms are gaining more popularity now a days as the algorithms are more efficient for complex problems. In this paper, we have explored the research work done by various researchers on regression testing using nature-inspired approaches. It is found that biology inspired computation e.g. genetic algorithm have been widely used in regression testing optimization with the intent of maximizing fault or code coverage in minimum time. It is also concluded that nature-inspired approaches have great potential to optimize regression testing problems.