Credit risk is one of the oldest forms of risk in the financial markets, and still revolutionary changes and developments are taking place in the credit markets today. This work contributes to the efforts of academics and practitioners to explain credit markets, price default related financial instruments such as defaultable fixed and floating rate debt, credit derivatives, and other securities with embedded credit risk. The whole process, from the specification of the underlying stochastic processes to the estimation of the parameters and calibration to market data is shown. The models proposed are validated in a lot of in- and out-of-sample statistical tests. Typical applications such as bond portfolio optimization under the consideration of credit risk are discussed in depth.