The accelerating race of digital computing technologies seems to be steering towards impasses—technological, economical and environmental—a condition that has spurred research efforts in alternative, 'neuromorphic' (brain-like) computing technologies. Furthermore, for decades, the idea of exploiting nonlinear physical phenomena 'directly' for non-digital computing has been explored under names like 'unconventional computing', 'natural computing', 'physical computing', or 'in-materio computing'. In this article I investigate coordinates and conditions for a generalized concept of 'computing' which comprises digital, neuromorphic, unconventional and possible future 'computing' paradigms. The main contribution of this paper is an in-depth inspection of existing formal conceptualizations of 'computing' in discrete-symbolic, probabilistic and dynamical-systems oriented views. It turns out that different choices of background mathematics lead to decisively different understandings of what 'computing' is. However, across this diversity a unifying coordinate system for theorizing about 'computing' can be distilled.