The ‘Third Wave’ of Human-Computer Interaction research extends beyond cognition and usage contexts to many aspects of user experience, including emotions, feelings, values and motivating worth. Design representations need to evolve, as existing task specification approaches are too limited. This paper motivates and presents User Experience Frames (UEFs), a representational resource for envisaging user experiences. UEFs support designing as connecting, which looks beyond crafting or conceptualising artefacts to a wide range of interdependent connections between designs, usage, outcomes, evaluations and beneficiaries. UEFs expose relationships between design qualities and unfolding user experiences. They connect the design qualities and emotional responses that are in focus for Kansei engineering, but extend beyond first impressions to the motivations that guide human choices.