Built upon a hierarchical access structure with primary and secondary users, opportunistic spectrum access resolves the inefficiency of the current command-and-control model of spectrum regulation while maintaining compatibility with legacy wireless systems. The basic idea is to allow secondary users to exploit instantaneous spectrum availability and communicate non-intrusively to primary users. While conceptually simple, opportunistic spectrum access presents challenges not encountered in conventional networks. Cognitive medium access control coupled with signal processing for identifying and exploiting instantaneous spectrum opportunities is one of the central technological underpinnings. This research develops algorithms and protocols for opportunistic spectrum access under energy and hardware constraints. The main scientific ideas being developed include (i) cognitive sensing and access strategies that learn from observations and offer improved performance over time, (ii) distributed protocol implementations in ad hoc networks without central controllers or dedicated communication/control channels, (iii) quantitative characterizations of the trade-off among optimality, complexity, and robustness of opportunistic spectrum access strategies. This research contributes to the advance of network science. It provides technical data for the assessment of the potentials of opportunistic spectrum access. Specific research topics arising from this project provide educational and research opportunities for undergraduate and graduate students.