Efficiently allocating the scarce and expensive radio resources is a key challenge for advanced radio communication systems. To this end, cognitive radio (CR) has emerged as a promising solution which can offer considerable improvements in spectrum utilization. Furthermore, cooperative communication is a concept proposed to obtain spatial diversity gains through relays without requiring multiple antennas. To benefit from both CR and cooperative communications, a combination of CR networks (CRNs) with cooperative relaying referred to as cognitive cooperative relay networks (CCRNs) has recently been proposed. CCRNs can better utilize the radio spectrum by allowing the secondary users (SUs) to opportunistically access spectrum, share spectrum with primary users (PUs), and provide performance gains offered by cooperative relaying. In this thesis, a performance analysis of underlay CRNs and CCRNs in different fading channels is provided based on analytical expressions, numerical results, and simulations. To allocate power in the CCRNs, power allocation policies are proposed which consider the peak transmit power limit of the SUs and the outage probability constraint of the primary network. Thus, the impact of multiuser diversity, peak transmit power, fading parameters, and modulation schemes on the performance of the CRNs and CCRNs can be analyzed. The thesis is divided into an introduction and five research parts based on peer-reviewed conference papers and journal articles. The introduction provides fundamental background on spectrum sharing systems, fading channels, and performance metrics. In the first part, a basic underlay CRN is analyzed where the outage probability and the ergodic capacity of the network over general fading channels is derived. In the second part, the outage probability and the ergodic capacity of an underlay CRN are assessed capturing the effect of multiuser diversity on the network subject to Nakagami-m fading. Considering the presence of a PU transmitter (PU-Tx), a power allocation policy is derived and utilized for CRN performance analysis under Rayleigh fading. In the third part, the impact of multiple PU-Txs and multiple PU receivers (PU-Rxs) on the outage probability of an underlay CCRN is studied. The outage constraint at the PU-Rx and the peak transmit power constraint of the SUs are taken into account to derive the power allocation policies for the SUs. In the fourth part, analytical expressions for the outage probability and symbol error probability for CCRNs are derived where signal combining schemes at the SU receiver (SU-Rx) are compared. Finally, the fifth part applies a sleep/wake-up strategy and the min(N; T) policy to an underlay CRN. The SUs of the network operate as wireless sensor nodes under Nakagami-m fading. A power consumption function of the CRN is derived. Further, the impact of M/G/1 queue and fading channel parameters on the power consumption is assessed.