Future fifth generation (5G) cellular networks have to cope with the expected ten-fold increase in mobile data traffic between 2015 and 2021. To achieve this goal, new technologies are being considered, including massive multiple-input multiple-output (MIMO) systems and millimeter-wave (mmWave) communications. Massive MIMO involves the use of large antenna array sizes at the base station, while mmWave communications employ frequencies between 30 and 300 GHz. In this thesis we study the impact of these technologies on the performance of channel estimators. Our results show that the characteristics of the propagation channel at mmWave frequencies improve the channel estimation performance in comparison with current, low frequency-based, cellular networks. Furthermore, we demonstrate the existence of an optimal angular spread of the multipath clusters, which can be used to maximize the capacity of mmWave networks. We also propose efficient noise variance estimators, which can be employed as an input to existing channel estimators.