Cremona groups are the groups of birational transformations of projective spaces. They have been the delight of algebraic geometers and group theorists in both, classical and modern times. Recently, geometric group theory and dynamics have opened up new viewpoints on the subject. In this talk, I will give a short introduction to Cremona groups and explain some natural constructions of isometric actions on negatively curved cube complexes. From those, we deduce old and new results. No prior knowledge of algebraic geometry nor geometric group theory will be assumed. This is joint work with Anne Lonjou.