The millimeter wave (mmWave) frequency band will become a key enabler for future wireless systems currently facing the explosive growth of data traffic and the sparsity of the traditional ultra-high frequency (UHF) band. Nevertheless, the challenges for mmWave communications lie in high propagation loss, sensitivity to blockage, high cost for equipping directional antennas, and so on. Furthermore, the traditional design for the UHF networks cannot be directly used for future mmWave networks, which needs to be reshaped from the perspectives of fundamental objectives, various constraints, and different degrees of freedom. This paper addresses the key functions and discusses the challenges for PHY layer and MAC layer design in mmWave small-cell networks, including mmWave antenna design, beamforming, initial access, radio resource allocation, power allocation, and so on. The novel resource management approach for the joint PHY-MAC layer design is proposed to find the trade-off among hardware cost of the mmWave antenna, beamforming overhead, and efficiency of the new resource block (RB) allocation in beam-frequency-time (B-T-F)-dimension. © 2013 IEEE.