Conceptual spaces have been proposed by Gärdenfors as an intermediate knowledge representation framework, sitting between high-level symbolic representations and low-level neural representations. While the theory of conceptual spaces has been influential in philosophy and cognitive science, to date it has seen relatively few applications within the field of Artificial Intelligence. One of the main stumbling blocks for such applications is that learning conceptual space representations in a purely data-driven way is challenging. In this talk, I will first give an overview of some approaches for learning conceptual space representations that have been developed within the context of the FLEXILOG project.