The theory of variations of Hodge structure has many applications in algebraic geometry. Most of these are based on the results by Schmid, Cattani, Kaplan, Kashiwara, and Kawai from the 1970s and 1980s. I will describe a new approach that proves these results -- such as the Hodge norm estimates or the nilpotent orbit theorem -- more easily (and that no longer requires quasi-unipotent local monodromy).