Millimeter-wave (mm-wave) communication is a key technology for future wireless networks. To combat significant path loss and exploit the abundant mm-wave spectrum, effective beamforming is crucial. Nevertheless, conventional fully digital beamforming techniques are inapplicable, as they demand a separate radio frequency (RF) chain for each antenna element, which is costly and consumes too much energy. Hybrid beamforming is a cost-effective alternative, which can significantly reduce the hardware cost and power consumption by employing a small number of RF chains. This paper presents a holistic view on hybrid beamforming for 5G and beyond mm-wave systems, based on a new taxonomy for different hardware structures. We take a pragmatic approach and compare different proposals from three key aspects: 1) hardware efficiency, i.e., the required hardware components; 2) computational efficiency of the associated beamforming algorithm; and 3) achievable spectral efficiency, a main performance indicator. Through systematic comparisons, the interplay and trade-off among these three design aspects are demonstrated, and promising candidates for hybrid beamforming in future wireless networks are identified.