Dynamical degrees are numerical invariants defined for dominant rational maps of projective varieties, measuring the complexity of the maps. Dynamical degrees are invariant under the birational conjugacy of maps, and these values are birational invariants in this sense. These invariants play a role in understanding the complexity and geometry of birational dynamical systems on projective varieties. On the projective spaces, the dynamical degrees are equal to the growth rate of the degrees of the homogeneous polynomials under iteration. In this talk, I will discuss the basic properties of dynamical degrees and relationships with other invariants defined for dominant rational maps, and introduce our recent results in this area.