This paper investigates power control and relay selection in Full Duplex Cognitive Relay Networks (FDCRNs), where the secondary-user (SU) relays can simultaneously receive data from the SU source and forward them to the SU destination. We study both non-coherent and coherent scenarios. In the non-coherent case, the SU relay forwards the signal from the SU source without regulating the phase; while in the coherent scenario, the SU relay regulates the phase when forwarding the signal to minimize the interference at the primary-user (PU) receiver. We consider the problem of maximizing the transmission rate from the SU source to the SU destination subject to the interference constraint at the PU receiver and power constraints at both the SU source and SU relay. We then develop a mathematical model to analyze the data rate performance of the FDCRN considering the self-interference effects at the FD relay. We develop low-complexity and high-performance joint power control and relay selection algorithms. Extensive numerical results are presented to illustrate the impacts of power level parameters and the self-interference cancellation quality on the rate performance. Moreover, we demonstrate the significant gain of phase regulation at the SU relay.