Millimeter wave (mmWave) communications has been considered one of the key techniques for the future generations of wireless systems due to the large mmWave bandwidth available. In order to reduce the hardware complexity and cost of mmWave transceivers, hybrid beamforming techniques have been developed, which rely on the channel state information (CSI) available to the receiver and/or transmitter. In mmWave channel estimation, the compressed sensing (CS)-based algorithms like orthogonal matching pursuit (OMP) have been widely studied to take the advantages of the sparse characteristics of mmWave channels. Specifically, the OMP-assisted adaptive codebook channel estimation has the merit of reduced implementation complexity, but it performs undesirably in low signal to noise ratio (SNR) scenarios. To circumvent this problem, we first develop an improved adaptive codebook channel estimation algorithm for orthogonal frequency division multiplexing (OFDM) mmWave systems, which enhances the estimation performance by exploiting the multi-carrier signals for joint decision making. Besides, we motivate to design the low-complexity and high-accuracy channel estimation methods for the mmWave systems employing OFDM signaling and hybrid transmitter/receiver beamforming. Specifically, a multi-layer sparse Bayesian learning (SBL) channel estimator is proposed to both improve the performance of channel estimation and reduce the complexity of signal processing. We compare the performance of the proposed channel estimator with that of a range of related channel estimators, including the OMP-, approximate message passing (AMP)- and conventional SBL-assisted channel estimators. Our studies show that the proposed adaptive codebook channel estimation algorithm in OFDM systems is capable of significantly improving the estimation accuracy at low SNR than the traditional adaptive codebook channel estimation algorithm. Besides, the proposed multi-layer SBL estimator is capable of achieving better performance than the benchmark estimators considered. Specifically, when compared with the traditional SBL estimator, the proposed multi-layer SBL estimator is capable of achieving a lower mean-square error (MSE), while simultaneously, requiring only about 1/10 of the computational complexity of the traditional SBL estimator. Then, the channel estimation in reconfigurable intelligent surface (RIS) assisted systems is studied. Recently, RIS has emerged as a key technology for increasing the capacity and extending the coverage of mmWave communications with low hardware cost and energy consumption. However, channel estimation is a challenge in the RIS-assisted systems since there is no signal processing module in the RIS in addition to the fact that there are a large number of the reflecting elements in the RIS. In this thesis, a low-complexity and high-accuracy channel estimation method is designed for the RIS-aided multi-user mmWave systems employing OFDM. Specifically, a multi-layer beam training aided SBL channel estimation algorithm is proposed to improve the accuracy and reduce the computational complexity of the RIS-aided system channel estimation. Our simulations show that the proposed channel estimation algorithm achieves a better performance than the benchmarkers in RIS-aided systems. Specifically, the normalized mean square error (NMSE) performance of the proposed algorithm is 3dB higher than the benchmarker algorithm when the computational complexity is 10 times less.