  Terahertz (THz) communications (THzCom) has experienced a meteoric rise of
interest, due to its benefits for ultra-high data rate transmission in the
sixth generation (6G) and beyond era. Despite so, the research on exploring the
potential of THzCom for other performance targets anticipated by 6G, including
massive connectivity and security, is still in its infancy. In this article, we
start with briefly describing the unique peculiarities of THz channels, and
then discuss theoretical frameworks to facilitate the analysis and design of
THz transmission for achieving massive connectivity and security. Then we
discuss promising spectrum management strategies, including the exploration of
multiple THz transmission windows and frequency reuse with multiplexing and
signal processing, to substantially increase the number of supported users and
identify to-be-tackled challenges. We further present important research
directions based on the principles of physical layer security, such as new
spectrum allocation policies and beamforming algorithms, to fight against
eavesdropping in THzCom systems, ushering in secure THzCom systems.
