Reconfigurable intelligent surface (RIS) assisted wireless systems require accurate channel state information (CSI) to control wireless channels and improve both the bandwidth and energy efficiency. However, CSI acquisition is non-trivial for two reasons: 1) the passive nature of RIS does not allow transceiving and processing pilot signals, and 2) the dimensions of the cascaded channel between transceivers increases with the large number of RIS elements, which yields high training overhead and computational complexity. While prior art has mainly focused on frequency-flat channel estimation, this paper proposes novel data-driven and compressive sensing based approaches for estimating both frequency-flat and frequency-selective cascaded channels of RIS-assisted multi-user millimeter-wave large multiple input multiple output (MIMO) systems with limited training overhead. The proposed methods exploit the common sparsity property among the different subcarriers and the double-structured sparsity property of the angular cascaded channel matrices as different angular cascaded channels observed by different users share completely common non-zero rows and user-specific column supports. The proposed data-driven cascaded channel estimation approaches use denoising neural networks to accurately detect channel supports. Alternatively, when data-training capabilities are not available, the compressive sensing based orthogonal matching pursuit (OMP) approach relies on sparsity properties and applies simultaneous OMP to detect the channel supports. Simulation results show that the pilot overhead required by the proposed scheme is lower than existing schemes. When compared to other OMP approaches that achieve an NMSE gap of 5 to 6 dB with respect to the Oracle least square lower bound, the proposed algorithms reduce the lower bound gap to only 1 dB, while reducing complexity by more than two orders of magnitude.