Random access techniques play a crucial role in machine-type communications (MTC), especially in the context of massive and sporadic device connectivity. Unlike traditional communication systems with scheduled access, random access allows devices to independently access the network without prior coordination. This flexibility is particularly beneficial for MTC scenarios where a large number of devices may transmit data sporadically. Unsourced random access (URA) is a form of grant-free random access in which devices remain entirely unidentified. As a result, there is no need for a codebook to store device identity preambles, whose dimension is squared to the number of connected users. This elimination of the codebook requirement empowers URA to efficiently accommodate an unbounded number of devices, reaching hundreds of millions of devices. This thesis proposes three unsourced random access algorithms suitable for Gaussian and wireless fading channels. First, we introduce a URA algorithm for use over Gaussian multiple access channels. In the proposed solution, the users are randomly separated by assigning varying levels of transmit power to each of them. This introduces power diversity, enhancing the system performance. In the second part, we offer a solution for URA over Rayleigh block-fading channels with a receiver equipped with multiple antennas. We employ a slotted structure with multiple stages of orthogonal pilots; each randomly picked from a codebook. In the proposed signaling structure, each user encodes its message using a polar code and appends it to the selected pilot sequences to construct its transmitted signal. The receiver employs an iterative algorithm to detect messages transmitted by different users. This algorithm comprises several components, including pi-lot detection, channel estimation, soft data detection, single-user polar decoder, and successive interference cancellation. Additionally, we improve this scheme by incorporating an efficient strategy that separates users by random grouping. Our extensive analytical and simulation results demonstrate the effectiveness of the proposed algorithm in terms of both energy efficiency and computational complexity. In the last part of the thesis, we study URA employing a passive reconfigurable intelligent surface, facilitating connections between the users and the base station when the direct link is blocked or significantly attenuated. We demonstrate through extensive simulations and analytical results that the pro-posed approach notably enhances system performance, particularly in channels with significant attenuation.