Status and Prospects of CKM Phase Determinations

We give an overview of direct determinations of the angles of the unitarity triangle of the CKM matrix, using CP-violating effects in B-meson decays. After a discussion of B --> pi K modes, which can be described efficiently through allowed regions in observable space and play an important role to determine gamma, we turn to extractions of the B^0_d -- bar{B^0_d} mixing phase phi_d, which equals 2 beta in the Standard Model, from B_d --> J/psi K_S, and emphasize that it is important to determine this phase unambiguously. Finally, we focus on B_d --> pi^+ pi^-, where recent B-factory data point towards large penguin contributions. The question arises now how the CP-violating observables of this mode can be transformed into information on the angles of the unitarity triangle. A promising tool to achieve this goal is offered by B_s --> K^+K^-, which is very accessible at hadronic B experiments, and allows a determination of phi_d and gamma. A variant for the e^+e^- B-factories is provided by B_d --> pi^{+/-} K^{+/-}, where data are already available, pointing to an exciting picture and a highly constrained allowed region in B_s --> K^+K^- observable space.