This chapter establishes foundational concepts for understanding digital gameful compositions (DGCs). It begins by defining ‘composition’ broadly, emphasising the collaborative and often indeterminate nature of musical works, particularly ‘open works’, which allow for performer agency. The chapter then surveys key definitions and attributes of games, highlighting how rule-based systems and player interaction shape meaning. Building on this, it examines analogue ‘game pieces’, concert works that incorporate game mechanics. Next, it explores interactive computer music. These works, which leverage real-time performer-computer interaction, foreground the role of human variability and cybernetic feedback in musical expression. The chapter concludes by introducing DGCs as a distinct category: interactive musical works structured by game systems and realised through performer engagement.