Reconfigurable Intelligent Surface (RIS) is a promising technology that is expected to play a significant role in the development of the next generation of wireless communications systems (i.e., 6G). RIS’s primary feature is its ability to control/optimize the propagation environment. Such a feature is quite desirable in wireless communications which explains the considerable research effort that has so far been put into RIS design and analysis. In spite of the growing interest in RIS technology, it takes time and resources to bring such a novel technology into practice. Such an investment requires RIS to offer a significant performance advantage over existing technologies. Therefore, to gain a deeper understanding of the potential theoretical performance enhancement of RIS compared to existing technologies, such as multiple-input and multiple-output (MIMO) or relay technology, and to explore practical ways to achieve this enhanced performance, it is imperative to first investigate the fundamental capacity limits of RISaided communication and then design algorithms to reach these limits. As our primary focus, we delve into the analysis of the ergodic capacity within RIS-aided MIMO communication systems, particularly when channel state information (CSI) is only available at the receiver. Additionally, we first consider lossless metasurfaces and various channel models to conduct a comprehensive analysis. Our analysis provides a diverse set of exact and asymptotic derivations, showcasing the influence of various parameters such as the number of antennas/RIS elements and signal-to-noise ratio (SNR) on the ergodic capacity of RIS-aided MIMO systems. The insights of each scenario are presented, and a key finding of this initial investigation is that arbitrary phase shift adjustments hold true when considering a lossless RIS and receive CSI only. In the subsequent scenario, we investigate the ergodic capacity of MIMO-RIS systems, incorporating more practical RIS models that account for the coupling between the phase and amplitude responses of each RIS element. As a result, various exact and asymptotic expressions are presented, each offering distinct insights. A significant observation emerges: arbitrary phase shift adjustment becomes sub-optimal, and instead, fixed phase shifts based on metasurface characteristics emerge as the optimal solution when CSI is only available at the receiver. Indeed, we demonstrate that the phase shift does not directly impact the ergodic capacity but rather influences it indirectly through the RIS amplitude response. As a final contribution, we focus on simplifying and optimizing the MIMO-RIS capacity when CSI is also available at the transmitter. Leveraging insights gained from capacity derivation and analysis in scenarios where CSI is only available at the receiver, we develop practical algorithms aimed at maximizing the MIMO-RIS capacity through passive beamforming in large systems. It turns out that in some scenarios, RIS phase optimization is equivalent to solving a classic MIMO beamforming problem, while in other scenarios, fixed phase shifts, based on metasurface characteristics, can provide optimal capacity.