Computation of the stable homotopy groups of spheres is a long-standing open problem in algebraic topology. I will introduce chromatic homotopy theory -- a powerful framework for organizing computations and describing large scale patterns in stable homotopy groups. It splits the problem into chromatic levels, and each level can be studied using the theory of formal group laws and their deformations. I will discuss the history of this field and some recent developments.

This is also the opening plenary talk of the Topology Festival.