Transport is frequently cited as one of the most expedient means by which humankind affects Earth's ecosystem. Indeed, as underscored by the Anthropocene proposition, transport-related impacts are significant to the point of resulting in alterations of the planet's geological structure. Rising awareness of such issues has led to increasing attention on the priority of achieving a radically decarbonised transport future. However, that vision stands in stark contrast to the aspirations of pro-space advocates who are in the process of initiating an alternate transport future facilitated by greatly increased - and highly carbon-intensive - access to outer space. This rapidly emerging 'beyond Earth' transport paradigm enormously expands the spatio-temporal boundaries of human transport and human impact. This article reviews prominent visions of desirable 'terrestrial' (Earth-bound) transport futures. We then critically consider the transport futures envisioned by advocates of space development. This enables us to construct a dialectics of two coexisting but sharply contrasting contemporary schools of thought. We identify a highly significant divide, with one set of discourses arguing for reigning in human influence while the other set seeks unfettered expansion. Our analysis indicates fundamental divergences in the assumptions and aims of terrestrial versus space-focussed transport discourses. We conclude that the largely unrecognised and unacknowledged tensions between these contrasting desirable transport futures will be difficult to resolve.