Our ability to predict, explain, or control sociotechnical realities is called into question by unprecedented phenomena in surveillance, in markets, and in other social and political domains. The apparatus of research – our current categories, instruments, arguments, and epistemic choices, rely on what is empirically accessible – on the past. Our research orientation to the future assumes continuity and the extension of past patterns into a predictable and thus manageable future. In this research we propose speculative engagement through digital geographies to make visible the processes of technological and cultural reconfiguration which result in unprecedented change. After describing the conception of ‘the future’ in widely used research methods, we describe speculative engagement as a research orientation to disclose new categories, relationships and values and a commitment to the performative relationships of our current research practices with potential future(s). Digital geographies are internally consistent and coherent worlds that are cognitively plausible but estranging. They are carriers of meaning and culture that underpin a broad class of methods to provide richly experienced ‘other worlds’. We posit principles for effective digital geographies and provide an illustrative example of a digital human artifact which estranges us from current assumptions. Finally, we argue that our approach enables researchers to engage with the future on its own terms. In this way researchers, designers and policy-makers can open current practices to new categories, relationships, logics and values and make visible the unprecedented reconfigurations in which our research is implicated.