We explore the role of narratives of complex systems in anti-cancer drug design. We set out the value of narratives relating to cancer in promoting awareness of risky behaviour and in supporting decision-making regarding treatment options. We present cancer as a dysregulated, complex system that has emergent behaviours at multiple scales, and is governed by dynamical spatio-temporal processes. We show that this system changes structure and function in response to anti-cancer drugs, and explain that these changes are sufficiently complex to impede effective drug design. We pose what narrative might offer to support the process of drug design, providing an example of work done to date that might serve as a foundation for narrating complexity. We suggest ways of using this work combined with that of others to begin to consider narrating drug design.