In multiuser systems the system resources must be divided among multiple users. This chapter develops techniques to allocate resources among multiple users and examines the fundamental capacity limits of multiuser systems. We know from Section 5.1.2 that signals of bandwidth B and time duration T occupy a signal space of dimension 2 BT. In order to support multiple users, the signal space dimensions of a multiuser system must be allocated to the different users. ^[1] Allocation of signaling dimensions to specific users is called multiple access. ^[2] Multiple access methods perform differently in different multiuser channels, and we will apply these methods to the two basic multiuser channels: downlink channels and uplink channels. Because signaling dimensions can be allocated to different users in an infinite number of different ways, multiuser channel capacity is defined by a rate region rather than a single number. This region describes all user rates that can be simultaneously supported by the channel with arbitrarily small error probability. We will discuss multiuser channel capacity regions for both the uplink and the downlink. We also consider random access techniques, whereby signaling dimensions are allocated only to active users, as well as power control, which ensures that users maintain the SINR required for acceptable performance. The performance benefits of multiuser diversity, which exploits the time-varying nature of the users channels, is also described. We conclude with a discussion of the performance gains and signaling techniques associated with multiple antennas in multiuser systems.