Many results in real and complex analysis are the consequence of mean value properties and theorems. This is the case for harmonic and holomorphic functions as well. The mean value property builds the foundation for several properties of each set of functions. Using this property one can derive more properties like the maximum principle for harmonic functions and the maximum modulus principle for holomorphic functions. These results are then used to show other properties. The goal is to compare the theorems and proofs for harmonic and holomorphic functions and to understand why the results seem to be similar.