The Anthropocene is proposed as a new interval of geological time in which human influence on Earth and its geological record dominates over natural processes. A major challenge in demarcating the Anthropocene is that the balance between human‐influenced and natural processes varies over spatial and temporal scales owing to the inherent variability of both human activities (as associated with culture and modes of development) and natural drivers (e.g. tectonic activity and sea level variation). Against this backdrop, we consider how geomorphology might contribute towards the Anthropocene debate by focusing on human impact on aeolian, fluvial, cryospheric and coastal process domains, and how evidence of this impact is preserved in landforms and sedimentary records. We also consider the evidence for an explicitly anthropogenic geomorphology that includes artificial slopes and other human‐created landforms. This provides the basis for discussing the theoretical and practical contributions that geomorphology can make to defining an Anthropocene stratigraphy. It is clear that the relevance of the Anthropocene concept varies considerably amongst different branches of geomorphology, depending on the history of human actions in different process domains. For example, evidence of human dominance is more widespread in fluvial and coastal records than in aeolian and cryospheric records, so geomorphologically the Anthropocene would inevitably comprise a highly diachronous lower boundary. Even to identify this lower boundary, research would need to focus on the disambiguation of human effects on geomorphological and sedimentological signatures. This would require robust data, derived from a combination of modelling and new empirical work rather than an arbitrary ‘war of possible boundaries' associated with convenient, but disputed, ‘golden’ spikes. Rather than being drawn into stratigraphical debates, the primary concern of geomorphology should be with the investigation of processes and landform development, so providing the underpinning science for the study of this time of critical geological transition. Copyright © 2016 John Wiley & Sons, Ltd.