The main goals of this project are to investigate optimal resource allocation policies for opportunistic and collaborative cognitive radio networks (CRNs), and to use such policies in the design of distributed and adaptive cross-layer protocols for CRNs. Through opportunistic access to the licensed spectrum, CRNs aim at improving spectrum efficiency, hence providing higher spatial reuse, programmable connectivity, and increased network availability. Our research agenda includes analytical formulations that aim at joint optimization of transmission powers, transmission rates, and spectrum in an opportunistic and distributed ad hoc CRN that is co-located with several primary (legacy) radio networks (PRNs). The presence of the PRNs impose frequency-dependent power masks on the transmissions of the CRN. Depending on channel dynamics (i.e., channel coherence time relative to the optimization window), we study a deterministic-control formulation for slowly varying channels as well as a stochastic-control formulation for fast varying channels. In both cases, the setup is general enough to allow for multi-channel, multi-path optimization at either the packet level or the session level. The optimized resource allocation strategies are used to develop distributed MAC and routing protocols for opportunistic CRNs under various settings and system constraints.