The challenge of understanding refugee movements is huge and affects countries worldwide on a daily basis. Yet, in terms of simulation, the challenge appears to have been largely ignored. I argue that we as researchers can, and should, harness our computational skills to better understand and predict refugee movements. I reflect on the computational challenges of modelling refugees, and present a simulation case study example focused on the Northern Mali Conflict in 2012. Compared to UNHCR data, the simulation predicts fewer refugees moving towards Mauritania, and more refugees moving towards Niger. This outcome aligns with UNHCR reports, which mention that unregistered refugees were known to reside outside of the official camps, though further investigations are required to rule out competing theories.