This talk asks the question: when can the cohomology of a variety be recovered from its tropicalisation? A class of motivating examples come from linear embeddings of complements of hyperplane arrangements into the torus and these examples have played an important role in tropical geometry. We will generalise upon these examples, by proving that a tropicalisation knows the cohomology of the original variety in a strong sense if and only if it satisfies local tropical Poincaré duality and the original variety is so-called “wunderschön”. This talk is based on joint work with Edvard Aksnes, Omid Amini, and Matthieu Piquerez.