Multiple access technology played an important role in wireless communication in the last decades: it increases the capacity of the channel and allows different users to access the system simultaneously. However, the conventional multiple access technology, as originally designed for current human-centric wireless networks, is not scalable for future machine-centric wireless networks. Massive access (studied in the literature under such names as massive-device multiple access, unsourced massive random access, massive connectivity, massive machine-type communication, and many-access channels) exhibits a clean break with current networks by potentially supporting millions of devices in each cellular network. The tremendous growth in the number of connected devices requires a fundamental rethinking of the conventional multiple access technologies in favor of new schemes suited for massive random access. Among the many new challenges arising in this setting, the most relevant are: the fundamental limits of communication from a massive number of bursty devices transmitting simultaneously with short packets, the design of low complexity and energy-efficient massive access coding and communication schemes, efficient methods for the detection of a relatively small number of active users among a large number of potential user devices with sporadic transmission pattern, and the integration of massive access with massive MIMO and other important wireless communication technologies. This paper presents an overview of the concept of massive access wireless communication and of the contemporary research on this important topic.