The next generation of communication systems, which is commonly referred to as 5G, is expected to support, besides the traditional voice and data services, new communication paradigms, such as Internet of Things (IoT) and Machine-to-Machine (M2M) services, which involve communication between Machine-Type Devices (MTDs) in a fully automated fashion, thus, without or with minimal human intervention. Although the general requirements of 5G systems are progressively taking shape, the technological issues raised by such a vision are still partially unclear. Nonetheless, general consensus has been reached upon some specific challenges, such as the need for 5G wireless access networks to support massive access by MTDs, as a consequence of the proliferation of M2M services. In this paper, we describe the main challenges raised by the M2M vision, focusing in particular on the problems related to the support of massive MTD access in current cellular communication systems. Then we analyze the most common approaches proposed in the literature to enable the coexistence of conventional and M2M services in the current and next generation of cellular wireless systems. We finally conclude by pointing out the research challenges that require further investigation in order to provide full support to the M2M paradigm.