Methods from geometric group theory have turned out to be essential tools to study Cremona groups. Especially isometric actions on spaces of negative or non-positive curvature have proven to be very useful. In this course\, we will focus on isometric actions of Cremona groups on CAT(0) cube complexes\, which allow us to better understand certain group theoretical and dynamical properties of groups of birational transformations. After a basic introduction to the geometry of CAT(0) cube complexes\, we construct several complexes with actions of Cremona groups. In a first step\, we look at the blow-up complex\, which allows us to give uniform proofs for various results about groups of birational transformations in dimension two. In a second step\, we construct cube complexes that allow isometric actions for groups of birational transformations in arbitrary dimension.