Machine-to-machine (M2M) communication has received increasing attention in recent year. An M2M network exhibits some salient features such as large number of machines/devices, low data rates, delay tolerant/sensitive, small packets, energy constrained and low or no mobility. A large number of M2M terminals may exist in a small area with many trying to simultaneously and randomly access for channel resources, which will result in overload and access problem. This increased signalling overhead and diverse requirements of machine-type communication (MTC) devices call for the development of flexible and efficient scheduling and random access techniques. In an M2M scenario, where the network is operating at high offered load with a large number of contending transmitters, distributed random access techniques are more appropriate than centralised scheduling techniques because of less control messages and better channel utilisation. There is a need for comparison of various medium access methods that can be used in the development of an efficient hybrid M2M and human to human network. In this article, we review and compare various scheduling and random access techniques in cellular networks, particularly in Long-Term Evolution. We also discuss how successful they are to fulfill the unique requirements of M2M communication and networking. Resource management in M2M networks with a large number of MTC devices is also discussed from the access point of view. Energy efficiency, being one of the main challenges of quality-of-service-constrained M2M communication, is also discussed. Minimisation of the energy consumption is tightly bound to channel access and hence considered in the comparison of various medium access control protocols. Finally, some potential research directions related to access control and resource allocation are presented for future work.