Since Mutation Testing was proposed in the 1970s, it has been considered as an effective technique of software testing process for evaluating the quality of the test data. In other words, Mutation Testing is used to evaluate the fault detection capability of the test data by inserting errors into the original program to generate mutations, and after then check whether tests are good enough to detect them. However, the problems of mutation testing such as a large number of generated mutants or the existence of equivalent mutants, are really big barriers for applying mutation testing. A lot of solutions have been proposed to solve that problems. A new form of Mutation Testing, Higher Order Mutation Testing, was first proposed by Harman and Jia in 2009 and is one of the most promising solutions. In this paper, we consider the main limitations of Mutation Testing and previous proposed solutions to solve that problems. This paper also refers to the development of Higher Order Mutation Testing and reviews the methods for finding the good Higher Order Mutants.