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Millimeter wave (mmW) communications is viewed as the key enabler of 5G cellular networks due to vast spectrum availability that could boost peak rate and capacity. Due to increased propagation loss in mmW band, transceivers with massive antenna array are required to meet a link budget, but their power consumption and cost become limiting factors for commercial systems. Radio designs based on hybrid digital and analog array architectures and the usage of radio frequency (RF) signal processing via phase shifters have emerged as potential solutions to improve radio energy efficiency and deliver performances close to the conventional digital antenna arrays. In this paper, we provide an overview of the state-of-the-art mmW massive antenna array designs and comparison among three array architectures, namely digital array, partially-connected hybrid array (sub-array), and fully-connected hybrid array. The comparison of performance, power, and area for these three architectures is performed for three representative 5G downlink use cases, which cover a range of pre-beamforming signal-to-noise-ratios (SNR) and multiplexing regimes. This is the first study to comprehensively model and quantitatively analyze all design aspects and criteria including: 1) optimal linear precoder, 2) impact of quantization error in digital-to-analog converter (DAC) and phase shifters, 3) RF signal distribution network, 4) power and area estimation based on state-of-the-art mmW circuits including baseband digital precoding, digital signal distribution network, high-speed DACs, oscillators, mixers, phase shifters, RF signal distribution network, and power amplifiers. Our simulation results show that the fully-digital array architecture is the most power and area efficient compared against optimized designs for sub-array and hybrid array architectures. Our analysis shows that digital array architecture benefits greatly from multi-user multiplexing. The analysis also reveals that sub-array architecture performance is limited by reduced beamforming gain due to array partitioning, while the system bottleneck of the fully-connected hybrid architecture is the excessively complicated and power hungry RF signal distribution network.