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In recent years, a new type of compilers and programming languages has emerged, called extensible compilers and programming languages. These new tools are created in hope to extend lifetime and usability of programming languages by allowing users to define new language constructs with their own syntax and semantics. In this paper we focus on a subset of extensible programming languages, called reflectively extensible programming languages that allow definition of syntax and semantics extensions to be mixed with regular code. To facilitate the creation of such compilers and languages, new parsing and semantic analysis algorithms are required. This paper analyses available extensible parsers, semantic analysers, compilers and highlights further possible research directions in this field. We find that existing parsing, semantic analysis methods, compilers and compiler generators are insufficient for implementation of reflectively extensible programming languages and that creation of new parsing and semantic analysis methods with specific qualities is required to facilitate such implementations.