With the rapid development and the increasing use of wireless devices, spectrum scarcity has become a problem. The higher frequencies have bad propagation characteristics and the lower frequencies have low data rates, therefore the radio spectrum that is available for efficient wireless transmission is a limited resource. One of the proposed solutions for this problem is cognitive relay networks (CRNs), where cognitive radio is combined with a cooperative spectrum sharing system to increase the spectrum utilization. In this thesis, the outage probability performances of underlay CRNs with interference power constraints from the primary network over Weibull fading channels have been investigated for three different scenarios. The maximum transmit power of the secondary network is governed by the maximum interference power that the primary network's receiver can tolerate. The first scenario is a cognitive dual-hop decode-and-forward (DF) relay network over independent non-identically distributed (i.n.i.d.) Weibull fading channels. In the second scenario, the CRN consists of a DF relay plus the direct link transmission with a selection combining receiver at the destination over i.n.i.d. Weibull fading channels. The third CRN considered has multiple DF relays where the best relay selection scheme is employed over independent identically distributed (i.i.d.) Weibull fading channels. The analytical results have been derived using the statistical characteristics of end-to-end signal-to-noise ratios, and have been verified by Monte-Carlo simulations.