Traditional approaches in the analysis of downlink systems decouple the precoding and the channel estimation problems. However, in cellular systems with mobile users, these two problems are, in fact, tightly coupled. In this paper, this coupling is explicitly studied by accounting for the channel training overhead and estimation error while determining the overall system throughput. This paper studies the problem of utilizing imperfect channel estimates for efficient linear precoding and user selection. It presents precoding methods that take into account the degree of channel estimation error. Information-theoretic lower and upper bounds are derived to evaluate the performance of these precoding methods. In typical scenarios, these bounds are close.