Credit default swaps (CDSs) are bilateral, derivative contracts that allow parties to shift the risk of default on an underlying obligation from a protection buyer to a protection seller. These instruments belong to the family of credit derivates and have become very popular in the last two decades. There are two types of CDSs: single-names and multi-names. The former are referenced to an individual corporate or sovereign borrower and the latter are based on various entities, for example an index of debtors or a basket of borrowers. CDSs help financial institutions to improve their risk diversification and can free regulatory capital, which can afterwards be used for other productive investments. Since the financial crisis, however, the role of CDSs has increasingly become the focus of the public attention. Frequently, the general opinion is negative and the risks resulting from these derivatives are commonly grossly overstated. The aim of this thesis is to analyze the CDS market in detail in order to take a serious look at the risks, benefits and disadvantages of CDSs. To be more precise, the market size, the market structure and the participants of the market are considered by using actual public available data. The data sources are mainly the Bank for International Settlement (BIS), the International Swaps and Derivatives Association (ISDA), and the Depository Trust & Clearing Corporation (DTCC). Furthermore, issues are presented which can lead to a distortion of the CDS market or the underlying bond market. These issues are supported by case examples. Finally, the two main credit modelling approaches are considered, one called the structural and the other called the reduced form. The market standard pricing model for marking CDS positions to market, which in is based on the latter approach, is used for valuing existing CDS positions. For this purpose, the author developed a Matlab programming code, which is included in the appendix of this thesis.