As an enabling mechanism for the implementation of cognitive radio networks (CRNs), cooperative sensing provides an effective approach for exploiting spectrum opportunities. Although extensive research has been carried out, the fundamental question in the context of cooperative sensing is still not well understood, which can be stated as follows: Given a set of sensors and a set of primary user (PU) channels for opportunistic usage, how are the sensors appropriately assigned to sense the PU channels? We refer to this problem as the cooperative sensing scheduling (CSS) problem. Specifically, the CRN's expected throughput achieved and the overhead incurred in the sensing procedure, i.e., the energy efficiency of the CRN, are jointly considered when we make scheduling decisions. We first study a homogeneous network scenario with the objective of maximizing the expected throughput of the CRN. The energy consumption of the CRN is subsequently taken into consideration. A theoretical framework is established to analyze the structures of the two cases, and algorithms guaranteeing the optimal solutions to be found are developed. With the insights gained, we extend the study to the heterogeneous case. Low-complexity algorithms are then presented, and their computation time and performance are compared with the optimal and existing approaches.