In this paper, we introduce Hebbian learning as a novel method for swarm robotics, enabling the automatic emergence of heterogeneity. Hebbian learning presents a biologically inspired form of neural adaptation that solely relies on local information. By doing so, we resolve several major challenges for learning heterogeneous control: 1) Hebbian learning removes the complexity of attributing emergent phenomena to single agents through local learning rules, thus circumventing the micro-macro problem; 2) uniform Hebbian learning rules across all swarm members limit the number of parameters needed, mitigating the curse of dimensionality with scaling swarm sizes; and 3) evolving Hebbian learning rules based on swarm-level behaviour minimises the need for extensive prior knowledge typically required for optimising heterogeneous swarms. This work demonstrates that with Hebbian learning heterogeneity naturally emerges, resulting in swarm-level behavioural switching and in significantly improved swarm capabilities. It also demonstrates how the evolution of Hebbian learning rules can be a valid alternative to Multi Agent Reinforcement Learning in standard benchmarking tasks.