How I learned to stop worrying and love motivic cohomology

The problem of constructing Galois cohomology classes with values in $p$-adic unipotent groups pervades the method of Chabauty--Kim. However, standard techniques, depending on finding ''enough'' points on the curve, run out of steam rather quickly, especially if one is interested in families of curves. We will present a systematic method for constructing the required classes using higher homotopy groups.