The emerging technology of machine-to-machine (M2M) communications is bringing a paradigm shift in healthcare delivery. A broad range of e-health applications can be conceived, with considerable benefits for both patients and healthcare providers. Many technological challenges have to be met, however, to ensure the widespread adoption of e-health solutions in the future. In this context, we aim to provide a comprehensive overview on M2M systems for e-health applications from a wireless communication perspective. We provide an overview of the candidate wireless technologies that are suitable for different parts of the M2M system architecture and then show how these technologies are seamlessly integrated to provide an end-to-end e-health solution. In particular, we discuss end-to-end solution designs and test bed implementations, we present the key security and privacy challenges associated with the sensitive nature of medical data, and we summarize the most recent research projects dedicated to e-health applications.