The purpose of this thesis is the study of portfolio credit risk models and the numerical methods applied for their computation. The Vasicek one-factor model will provide a point of departure, allowing us to study its generalization and the development of a numerical method for its computation. Subsequently, we present the large portfolio approximation and its generalization. These methodologies and especially their generalizations will require the use of advanced numerical methods whose implementation will be explained in detail. Furthermore, we include other more sophisticated methodologies, such as the Fourier transform method or the Haar wavelet approximation, which consider portfolios with exposure concentrations and loss given default. A detailed study of their respective implementations will be presented for both methodologies. Finally, we present a comparative study of methods in order to identify the most appropriate method for each type of portfolio.