With diverse applications in mathematics, physics, and finance, Random Matrix Theory (RMT) has recently attracted a great deal of attention. While Hermitian RMT is of special importance in physics because of the Hermiticity of operators associated with observables in quantum mechanics, non-Hermitian RMT has also attracted a considerable attention, in particular because they can be used as models for dissipative or open physical systems. However, due to the absence of a simplifying symmetry, the study of non-Hermitian random matrices is, in general, a diffcult task. A special subset of non-Hermitian random matrices, the so-called random normal matrices, are interesting models to consider, since they offer more symmetry, thus making them more amenable to analytical investigations. By definition, a normal matrix M is a square matrix which commutes with its Hermitian adjoint, i.e., (M, M (1)). In this thesis, we present a novel derivation of extreme value statistics (EVS) of Hermitian random matrices, namely the approach of orthogonal polynomials, to normal random matrices and 2D Coulomb gases in general. The strength of this approach is its physical and intuitive understanding. Firstly, this approach provides an alternative derivation of results in the literature. Precisely speaking, we show convergence of the rescaled eigenvalue with largest modulus of a Ginibre ensemble to a Gumbel distribution, as well as universality for an arbitrary radially symmetric potential which meets certain conditions. Secondly, it is shown that this approach can be generalised to obtain convergence of the eigenvalue with smallest modulus and its universality at the finite inner edge of the eigenvalue support. One interesting aspect of this work is the fact that we can use standard techniques from Hermitian random matrices to obtain the EVS of non-Hermitian random matrices.