The current demands for extremely high data rate wireless services and the spectrum scarcity at the sub-6 GHz bands are forcefully motivating the use of the millimeter-wave (mmWave) frequencies. MmWave communications are characterized by severe attenuation, sparse-scattering environment, large bandwidth, high penetration loss, beamforming with massive antenna arrays, and possible noiselimited operation. These characteristics imply a major difference with respect to legacy communication technologies, primarily designed for the sub-6 GHz bands, and are posing major design challenges on medium access control (MAC) layer. This book chapter discusses key MAC layer issues at the initial access and mobility management (e.g., synchronization, random access, and handover) as well as resource allocation (interference management, scheduling, and association). The chapter provides an integrated view on MAC layer issues for cellular networks and reviews the main challenges and trade-offs and the state-of-the-art proposals to address them.