The focus of sensemaking research is often on process and resources such as "schemas" and "frames". Less attention has been paid to the conceptual structures that make up the schema or frame, or how visualisations can be designed to support users' conceptual structures. In this chapter, we present an approach to gathering user requirements based on the conceptual structures that people are working with when making sense of a domain. We illustrate the approach with examples drawn from our own experience of designing, prototyping and testing an interactive visualisation tool for making sense of academic literature and of studies of sensemaking by lawyers and journalists. We discuss how to move from requirements to design, drawing on a classification of visualisations that highlights their principal conceptual structuring basis. Since each individual makes sense in their own way, it is beneficial to include features that enable people to work with a representation in their own way; for this, appropriation tools are helpful. We discuss the design of such features. Finally, we present an approach to evaluating interactive visualisations in terms of their support for sensemaking, focusing on the quality of the fit between users and system.