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Future cellular networks will use millimeter wave (MMW) spectrum to enable extremely high data rates. Although this spectrum offers numerous significant performance improvements in wireless networks, MMW frequencies also have unique propagation characteristics and hardware constraints, which require revisiting the prior channel modeling and system design. In this thesis, we develop a geometry-based stochastic channel model to characterize the effect of the first-order reflection paths. We consider random locations, sizes and orientations of buildings and derive a closed-form expression for the power delay profile contributed by the first-order reflection paths. We show that wireless networks can benefit from buildings in the communication area, as the external building surfaces render reflection paths whose signal powers are comparable to that of the direct path. Dense base station (BS) deployments are required to overcome the signal losses due to blockages, which unfortunately introduce additional interference at the receiver. We propose a BS coordination scheme to improve the user performance in the dense MMW cellular networks. We derive expressions for the signal-to-interference and noise ratio (SINR) coverage probability and area spectral efficiency (ASE) by incorporating the peculiarity characteristics of MMW communications. Our results show a significant improvement in performance in terms of SINR coverage probability and ASE. In this thesis, we also investigate the uplink performance of the MMW cellular networks. We model the locations of users as of a Poisson cluster process and develop an analytical expression to evaluate the SINR coverage probability. We study the performances of a typical BS for two association strategies, i.e., the closest-selection (CS) and the strongest-selection (SS). Our results show that regarding SINR coverage probability, the SS strategy outperforms the CS strategy in the environment with dense blockages.