To self-organise into complex structures such as tissues and organs, individual cells need to interact. A generic mechanism for this interaction is a chemical signalling. The ability of an individual cell to follow a gradient of chemicals is called chemotaxis. Starting from a microscopic description of chemotactic cells, I will present a coarse-graining procedure to describe an assembly of such particles. This system exhibits a phase transition that I will then study using a dynamical renormalisation group approach. This analysis indicates the crucial role of a polarized chemotactic interaction, usually overlooked in phenomenological approaches. Finally, I will discuss an emergent symmetry of the model that allows us to compute scaling exponents exactly. In particular, we deduce a superdiffusive behavior of the particle density fluctuations in all physical dimensions.