This PhD thesis studies and contributes to the literature regarding central bank independence and central bank transparency. The thesis is split into three parts with the first part (which coincides with the first chapter of the thesis) providing in-depth reviews of the issues and key papers of both the theoretical and empirical literature on the central bank independence and transparency. Furthermore, there is an extensive review of the goals and functions of the European Central Bank (ECB) as well a short survey concerning the issues of independence and transparency of the ECB. In the second part we examine how wage indexing affects the optimal degree of central bank conservativeness. In particular, in the third chapter of the thesis we develop a theoretical model when there is a monopoly worker union in the economy which is explicitly inflation-averse and examine how wage indexing affects the optimal degree of central bank conservativeness. In the fourth chapter we study the same issue but in a dynamic setting where the economy is characterized by employment persistence. In the third part we examine the relationship between central bank independence, central bank transparency and public debt policy. In particular, in the fifth chapter we empirically estimate the relationship between central bank transparency and the percentage of nominal debt for various OECD countries. In the sixth chapter we develop a theoretical model where we examine the inter-relationships between central bank independence, transparency and public debt issuing policy. The last part of the thesis reviews the results of the thesis and draws conclusions and recommendations towards the ECB.