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This dissertation aims on analyzing fundamental concepts and dogmas of a graph-based genetic programming approach called Cartesian Genetic Programming (CGP) and introduces advanced genetic operators for CGP. The results of the experiments presented in this thesis lead to more knowledge about the algorithmic use of CGP and its underlying working mechanisms. CGP has been mostly used with a parametrization pattern, which has been prematurely generalized as the most efficient pattern for standard CGP and its variants. Several parametrization patterns are evaluated with more detailed and comprehensive experiments by using meta-optimization. This thesis also presents a first runtime analysis of CGP. The time complexity of a simple (1+1)-CGP algorithm is analyzed with a simple mathematical problem and a simple Boolean function problem. In the subfield of genetic operators for CGP, new recombination and mutation techniques that work on a phenotypic level are presented. The effectiveness of these operators is demonstrated on a widespread set of popular benchmark problems. Especially the role of recombination can be seen as a big open question in the field of CGP, since the lack of an effective recombination operator limits CGP to mutation-only use. Phenotypic exploration analysis is used to analyze the effects caused by the presented operators. This type of analysis also leads to new insights into the search behavior of CGP in continuous and discrete fitness spaces. Overall, the outcome of this thesis leads to a reconsideration of how CGP is effectively used and extends its adaption from Darwin's and Lamarck's theories of biological evolution.