Driven by the demand for bandwidth-hungry multimedia and internet-related wireless data applications, communication engineers seek to maximally exploit the spectral resources in all available dimensions. Two approaches, cognitive radio (cognition) and cooperative communications (cooperation), have been recently shown to be able to significantly improve the spectral efficiency. In this dissertation, we evaluate the capacity gains of the Gaussian interference channel by using either a cognition or cooperation approach. For cognitive radio, we consider a MIMO Gaussian Z-interference channel (ZIC) as shown in Fig. 1.2, when transmit node C has imperfect cognitive knowledge of the signal sent by transmit node A. First, we compute the capacity of this channel assuming non-causal but noisy knowledge at node C of node A's signal. We then compute the achievable rate for a causal cognitive strategy: This achievable rate is derived using a two-phase transmission scheme in which node C uses a combination of a linear minimum mean square error (LMMSE) estimator and dirty paper code and node D employs a combination of LMMSE estimator and partial interference canceler. The achievable rate is studied in two different cases: (i) Node C operates in full-duplex mode and (ii) Node C operates in half-duplex mode. To quantify the performance of the proposed strategy, we compute simple lower and upper bounds on the capacity of this channel. Similar to interference channel, the achievable rate of the cognitive ZIC varies non-monotonically with the interference. Specifically, the achievable rate first decreases with the channel gain between nodes A and D and then begins to increase beyond a certain threshold. The difference in achievable rate between full-duplex and half-duplex transmission is also numerically evaluated. For cooperative communication, we evaluate the capacity region of a two user Gaussian interference channel with node cooperation. We develop half-duplex schemes and their respective achievable regions and upper bounds for the case when the system allows transmitter cooperation (TXC) only, receiver cooperation (RXC) only and both transmitter and receiver cooperation (TXRXC). We show that by using our TXC scheme, there is significant capacity improvement compared to the previous results, especially when the cooperation link is strong. Further, we quantify the sum rate increase of TXC, RXC and TXRXC with respect to the cooperation channel gain. If the cooperation channel gain is infinity, the rates of all three schemes achieve their respective outer bounds. It is also shown that TXC provides larger capacity gain over RXC under the same channel and power conditions. With both TXRXC, significant gain in achievable rates can further be reaped over TXC. We also investigate another common cooperative communication strategy, i.e., the cooperation by relays. We introduce a channel model called the Multi-source Multi-relay channel. In this channel, the transmit signals of all users are received at multiple distinct relays. Each of these transmit signals can be either decode-and-forward (DF) or amplify and forward (AF) at any one or a combination of the relays to the destination. We compute the achievable regions for both DF and AF strategies and compare them under various channel scenarios.