Deep Learning (DL) has been successfully applied to a wide range of application domains, including safety-critical ones. Several DL testing approaches have been recently proposed in the literature but none of them aims to assess how different interpretable features of the generated inputs affect the system's behaviour. In this paper, we resort to Illumination Search to find the highest-performing test cases (i.e., misbehaving and closest to misbehaving), spread across the cells of a map representing the feature space of the system. We introduce a methodology that guides the users of our approach in the tasks of identifying and quantifying the dimensions of the feature space for a given domain. We developed DeepHyperion, a search-based tool for DL systems that illuminates, i.e., explores at large, the feature space, by providing developers with an interpretable feature map where automatically generated inputs are placed along with information about the exposed behaviours.