Tools have coined human life, living conditions, and culture. Recognizing the cognitive architecture underlying tool use would allow us to comprehend its evolution, development, and physiological basis. However, the cognitive underpinnings of tool mastering remain little understood in spite of long-time research in neuroscientific, psychological, behavioral and technological fields. Moreover, the recent transition of tool use to the digital domain poses new challenges for explaining the underlying processes. In this interdisciplinary review, we propose three building blocks of tool mastering: (A) perceptual and motor abilities integrate to tool manipulation knowledge, (B) perceptual and cognitive abilities to functional tool knowledge, and (C) motor and cognitive abilities to means-end knowledge about tool use. This framework allows for integrating and structuring research findings and theoretical assumptions regarding the functional architecture of tool mastering via behavior in humans and non-human primates, brain networks, as well as computational and robotic models. An interdisciplinary perspective also helps to identify open questions and to inspire innovative research approaches. The framework can be applied to studies on the transition from classical to modern, non-mechanical tools and from analogue to digital user-tool interactions in virtual reality, which come with increased functional opacity and sensorimotor decoupling between tool user, tool, and target. By working towards an integrative theory on the cognitive architecture of the use of tools and technological assistants, this review aims at stimulating future interdisciplinary research avenues.