In term of Compiler optimization, classical compilers implemented with an effective optimization technique called Peephole optimization. In the early stage of the implementation of this technique basically applied using string pattern matching performed on the regular expression and which are known as classical peephole optimizers. In the classical optimizers, the string pattern matching approach is considered as a processing of the input of the syntax of assembly code but its meaning gets lost. This paper explores prior research and current research issues in term of 'Optimizing' compilers with the implementation of Peephole optimization using different pattern matching approach that focuses on regular expression. In several research discussed below targets the implementation of pattern matching approach based on rule application strategy to achieve optimization of assembly code syntax for specific machine or retargetable [machine independent] in context of structured programming, procedure oriented programming and Object Oriented Programming.