Millimeter wave (mmWave) communications are gaining significant attention due to their potential to achieve high data rates of multiple Gbps per user. While mmWave is suitable for stationary scenarios like indoor hotspots or backhaul, it poses challenges in mobile networks due to movement of nodes, complex channel structures, and coordination difficulties. This paper provides a comprehensive survey of mmWave communications for future mobile networks (5G and beyond), covering channel measurements, MIMO transceiver design, multiple access, backhauling, coverage, and standardization. It discusses the technical challenges and potentials of mmWave, including severe pathloss, high penetration loss, high power consumption, and hardware impairments. The paper also highlights the benefits of mmWave, such as large available bandwidth, short wavelength, and narrow beamwidth, which enable high security and resilience against interference. The paper reviews various channel measurement campaigns and models, including the 3GPP Spatial Channel Model, WINNER I/II/+ models, and COST 273/2100 models. It also discusses MIMO design for mmWave communications, including hybrid analog-digital architectures, channel estimation, and beam-training techniques. The paper concludes that mmWave communications have the potential to revolutionize future mobile networks by providing high data rates, low latency, and high spectral efficiency.Millimeter wave (mmWave) communications are gaining significant attention due to their potential to achieve high data rates of multiple Gbps per user. While mmWave is suitable for stationary scenarios like indoor hotspots or backhaul, it poses challenges in mobile networks due to movement of nodes, complex channel structures, and coordination difficulties. This paper provides a comprehensive survey of mmWave communications for future mobile networks (5G and beyond), covering channel measurements, MIMO transceiver design, multiple access, backhauling, coverage, and standardization. It discusses the technical challenges and potentials of mmWave, including severe pathloss, high penetration loss, high power consumption, and hardware impairments. The paper also highlights the benefits of mmWave, such as large available bandwidth, short wavelength, and narrow beamwidth, which enable high security and resilience against interference. The paper reviews various channel measurement campaigns and models, including the 3GPP Spatial Channel Model, WINNER I/II/+ models, and COST 273/2100 models. It also discusses MIMO design for mmWave communications, including hybrid analog-digital architectures, channel estimation, and beam-training techniques. The paper concludes that mmWave communications have the potential to revolutionize future mobile networks by providing high data rates, low latency, and high spectral efficiency.