The thesis is dedicated to studying methods to improve the efficiency of random access schemes and to facilitate their deployment in machine-type communications (MTC). First, a joint user activity identification and channel estimation scheme is designed for grant-free random access systems. We propose a decentralized transmission control and design a compressed sensing (CS)-based user identification and channel estimation scheme. We analyze the packet delay and throughput of the proposed scheme. We also optimize the transmission control scheme to maximize the system throughput. Second, a random access scheme, i.e., the coded slotted ALOHA (CSA) scheme, is designed for erasure channels to improve the system throughput. By deriving the extrinsic information transfer (EXIT) functions and optimizing their convergence behavior, we design the code probability distributions for CSA schemes with repetition codes and maximum distance separable (MDS) codes to maximize the expected traffic load, under packet erasure and slot erasure channels. We derive the asymptotic throughput of CSA schemes over the erasure channels for an infinite frame length, which is verified to well approximate the throughput for a practical frame length. Third, an efficient data decoding algorithm for the CSA scheme is proposed to further improve the system efficiency. We present a low-complexity physical-layer network coding (PNC) method to obtain linear combinations of collided packets and design an enhanced message-level successive interference cancellation (SIC) algorithm to exploit the linear combinations of collided packets. We propose an analytical framework and derive the system throughput for the proposed scheme. The CSA scheme is further optimized to maximize the system throughput and energy efficiency.