This chapter addresses the connectivity problem between a massive number of intermittently active devices contending for transmission of short uplink packets to a single base station. Such a context, usually referred to as 'massive multiple access', deviates sharply from traditional multiple access due to the extremely large device population size, random devices' activity, transmission of short packets, and bursty nature of transmissions from the generic device. Massive multiple access problems have fostered a revival of random access theory and techniques as well as the development of sophisticated grant-free access schemes featuring a tight interaction between the the physical and the medium access control layers. The chapter describes massive multiple access challenges towards sixth-generation mobile networks and overviews promising technologies and research directions.