In this article, the new term, namely beam-space multiplexing, is proposed for the former multi-layer beamforming for 4G TD-LTE in 3GPP releases. We provide a systematic overview of beam-space multiplexing from engineering and theoretical perspectives. Firstly, we clarify the fundamental theory of beam-space multiplexing. Specifically, we provide a comprehensive comparison with the antenna-space multiplexing in terms of theoretical analysis, channel state information acquisition, and engineering implementation constraints. Then, we summarize the key technologies and 3GPP standardization of beam-space multiplexing in 4G TD-LTE and 5G new radio (NR) in terms of multi-layer beamforming and massive beamforming, respectively. We also provide system-level performance evaluation of beam-space multiplexing schemes and field results from current commercial TD-LTE networks and field trial of 5G. The practical deployments of 4G TD-LTE and 5G cellular networks demonstrate the superiority of beam-space multiplexing within the limitations of implementation complexity and practical deployment scenarios. Finally, the future trends of beam-space multiplexing in 6G and beyond are discussed, including massive beamforming for extremely large-scale MIMO (XL-MIMO), low earth orbit (LEO) satellites communication, data-driven intelligent massive beamforming, and multi-target spatial signal processing, i.e., joint communication and sensing, positioning, etc.