Many polynomials arising in combinatorics are known or conjectured to have only real roots. One approach to these questions is to study transformations that preserve the real-rootedness property. This talk is centered around the Eulerian transformation which is the linear transformation that sends the i-th standard monomial to the i-th Eulerian polynomial. Eulerian polynomials appear in various guises in enumerative and geometric combinatorics and have many favorable properties, in particular, they are real-rooted and symmetric. We discuss how these properties carry over to the Eulerian transformation. In particular, we disprove a conjecture by Brenti (1989) concerning the preservation of real roots, extend recent results on binomial Eulerian polynomials and provide enumerative and geometric interpretations. This is joint work with Petter Brändén.