Debates regarding the nature and role of HCI research and practice have intensified in recent years, given the ever increasingly intertwined relations between humans and technologies. The framework of Human-Engaged Computing (HEC) was proposed and developed over a series of scholarly workshops to complement mainstream HCI models by leveraging synergy between humans and computers with its key notion of "engagement". Previous workshop meetings found "engagement" to be a constructive and extendable notion through which to investigate synergized human-computer relationships, but many aspects concerning the core concept remain underexplored. This SIG aims to tackle the notion of engagement considered through discussions of four thematic threads. It will bring together HCI practitioners and researchers from different disciplines including Humanities, Design, Positive Psychology, Communication and Media Studies, Neuroscience, Philosophy and Eastern Studies, to share and discuss relevant knowledge and insights and identify new research opportunities and future directions.