Machine-to-machine (M2M) communication is becoming an increasingly important part of mobile traffic and thus also a topic of major interest for mobile communication research and telecommunication standardization bodies. M2M communication offers various ubiquitous services and is one of the main enablers of the vision inspired by the Internet of Things (IoT). The concept of mobile M2M communication has emerged due to the wide range, coverage provisioning, high reliability, and decreasing costs of future mobile networks. Nevertheless, M2M communications pose significant challenges to mobile networks, e.g., due to the expected large number of devices with simultaneous access for sending small-sized data, and a diverse application range. This paper provides a detailed survey of M2M communications in the context of mobile networks, and thus focuses on the latest Long-Term Evolution-Advanced (LTE-A) networks. Moreover, the end-to-end network architectures and reference models for M2M communication are presented. Furthermore, a comprehensive survey is given to M2M service requirements, major current standardization efforts, and upcoming M2M-related challenges. In addition, an overview of upcoming M2M services expected in 5G networks is presented. In the end, various mobile M2M applications are discussed followed by open research questions and directions.