Even while they have been subject to critique, maps and mapping processes have been widely taken up as creative and critical tools. This has not been the case with clocks. ‘Clock time’ is widely used as a shorthand phrase to refer to the time of regularity, punctuality, linearity and normalisation. Contrasted unfavourably with more nuanced non-linear accounts of temporal consciousness, the clock primarily serves as a symbol of oppression, rather than a device with liberatory potential. This article offers an account of why this might be the case and what possibilities there might be for clocks to challenge and transform dominant structures of temporal practice. Looking first to continental philosophy, which is widely recognised as a key resource for thinking through the politics of time, we find that clocks are so closely associated with ‘objective time’ that they are often summarily dismissed and placed outside the sphere of concern. Looking more closely at cases where the operationalization of clock-time has come under wide public debate, I show that the conception of clock-time utilised by continental philosophers is fundamentally inaccurate. Instead I call attention to the wide body of work that shows how clocks are shaped by power, politics and technological need. This mutability of clock-time suggests that, despite their dismissal within continental philosophy, clocks have the potential to be utilised in unexpected ways. Calling for the development of a critical horology, as a sister discipline to critical cartography, the rest of this paper looks at the potential role of ‘temporal design’ (Pschetz et al 2016) in its development. Here we see artists, designers and activists are indeed turning to the clock as a way of intervening into social, ethical, political and environmental issues.