Machine-type communications (MTC) are expected to play an essential role within future 5G systems. In the FP7 project METIS, MTC has been further classified into "massive Machine-Type Communication" (mMTC) and "ultra-reliable Machine-Type Communication" (uMTC). While mMTC is about wireless connectivity to tens of billions of machine-type terminals, uMTC is about availability, low latency, and high reliability. The main challenge in mMTC is scalable and efficient connectivity for a massive number of devices sending very short packets, which is not done adequately in cellular systems designed for human-type communications. Furthermore, mMTC solutions need to enable wide area coverage and deep indoor penetration while having low cost and being energy efficient. In this article, we introduce the physical (PHY) and medium access control (MAC) layer solutions developed within METIS to address this challenge.