Abstract：This talk focuses on self-organised crystalline phases experimentally realized in a system with a BEC dispersively coupled to a high-finesse optical cavity and transversally illuminated by a pump laser beam. Self-organization phase is interesting from a condensed matter viewpoint as it features a cavity-mediated long-range atom-atom interaction and allows real-time access to the system dynamics via the leakage of the cavity photon field. This system thus provides an ideal platform for studying the universalities of phase transitions such as symmetry breaking and critical behaviours. I will first introduce the generation of the self-organised crystal via a superradiant phase transition and its general properties. I will then talk about our recent experiment on a first order structural phase transition between two different self-organised crystalline phases. we study the transition in real time using quantum optical methods and observe a transient dynamics of the system after the phase transition. This goes beyond equilibrium thermodynamics.