Selected Theoretical Issues in B-meson Physics: CKM matrix and Semileptonic Decays

These notes are a written version of a lecture given at the International Seminar {\it Modern Trends and Classical Approach} devoted to the 80$^{th}$ anniversary of Prof. Karen Ter-Martirosyan, ITEP September 30 -- October 1, 2002. The notes represent a non-technical review of our present knowledge on the phenomenology of weak decays of quarks, and their r\^ole in the determination of the parameters of the Standard Model. They are meant as an introduction to some of the latest results and applications in the field. Specifically, we focus on CP violation in B-decays and the determination of the CKM matrix element $V_{cb}$ from semileptonic decays of $B$ mesons. We also briefly discuss phenomenological applications concerning the electron-energy spectra in semileptonic $B$ and $B_c$ decays.