Summary
Dipolar Bose-Einstein condensates emerged as a unique platform permitting the exploration of nonlinear dynamics at the classical-quantum interface, phase-transitions and the realization of supersolidity. In this talk we present theoretical results discussing self-organized pattern-formation in this system, which can proceed via a first- or second-order phase-transition. We show how competing nonlinearities that contain crucial beyond mean-field contributions can give rise to new stable and metastable phases of matter and discuss finite temperature effects.