The paper introduces Joint Spatial Division and Multiplexing (JSDM), a novel approach to multiuser MIMO downlink that leverages the correlation structure of channel vectors to enable a large number of antennas at the base station while requiring reduced-dimensional Channel State Information at the Transmitter (CSIT). This reduces the overhead of downlink training and CSIT feedback, making JSDM suitable for Frequency Division Duplexing (FDD) systems, where uplink-downlink channel reciprocity cannot be exploited. JSDM involves two stages: pre-beamforming and MU-MIMO precoding. The pre-beamforming matrix depends only on the channel second-order statistics, while the MU-MIMO precoding matrix is based on the instantaneous knowledge of the reduced-dimensional "effective" channels. The paper proves that under certain conditions, JSDM incurs no loss of optimality compared to full CSIT. For linear uniformly spaced arrays, these conditions are met when the number of antennas is large, and a DFT-based pre-beamforming scheme is proposed. The paper also extends JSDM to two-dimensional antenna arrays and three-dimensional beamforming, achieving attractive performance in realistic scenarios. The analysis is supported by numerical results obtained using a deterministic equivalent approximation, which avoids heavy Monte Carlo simulations.The paper introduces Joint Spatial Division and Multiplexing (JSDM), a novel approach to multiuser MIMO downlink that leverages the correlation structure of channel vectors to enable a large number of antennas at the base station while requiring reduced-dimensional Channel State Information at the Transmitter (CSIT). This reduces the overhead of downlink training and CSIT feedback, making JSDM suitable for Frequency Division Duplexing (FDD) systems, where uplink-downlink channel reciprocity cannot be exploited. JSDM involves two stages: pre-beamforming and MU-MIMO precoding. The pre-beamforming matrix depends only on the channel second-order statistics, while the MU-MIMO precoding matrix is based on the instantaneous knowledge of the reduced-dimensional "effective" channels. The paper proves that under certain conditions, JSDM incurs no loss of optimality compared to full CSIT. For linear uniformly spaced arrays, these conditions are met when the number of antennas is large, and a DFT-based pre-beamforming scheme is proposed. The paper also extends JSDM to two-dimensional antenna arrays and three-dimensional beamforming, achieving attractive performance in realistic scenarios. The analysis is supported by numerical results obtained using a deterministic equivalent approximation, which avoids heavy Monte Carlo simulations.