This chapter investigates the performance of primary and secondary users in a spectrum-sharing cognitive environment. In this setup, multiple secondary users compete to share a channel dedicated to a primary user in order to transmit their data to a receiver unit. One secondary user is scheduled to share the channel, and to do so, its transmission power should satisfy the outage probability requirement of the primary user. Secondary users are ranked according to their channel strength, and performance measures are derived as a function of a generic channel rank. The performance of different scheduling schemes is also investigated. Further, the performance of the primary user is investigated in this environment. Numerical results are presented to verify the theoretical analysis and investigate the relation between the parameters of the communication environment and the performance measures of the users of the system.