We consider the application of different time-reversal (TR) signal processing and beamforming techniques to multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) wireless communication systems. Conventional TR beamforming provides spatial focusing at the intended receiver; however, it does not yield perfect channel equalization. Time-reversed pilot can be normalized to provide perfect equalization at the expense of power level. This equalization is particularly important for high data rates where the bit error rate performance is dominated by internal noise due to intersymbol interference. To increase physical layer covertness, TR beamforming is combined with the multiple-signal-classification (MUSIC) technique to produce null fields at eavesdroppers. This technique is also applied to MIMO setups to eliminate interuser interference and hence increase system capacity. Differential TR is used to obtain and update pilot signals for passive moving receivers, i.e., those that cannot (or do not) transmit pilot signals. Time-reversed differential backscattered signal is able to provide satisfactory spatial and temporal focusing at the moving receiver.