The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class over the moduli space of stable curves. The r-ELSV formula is a conjecture that generalizes ELSV to the space of curves endowed with r-spin structures, that is, r-th tensor roots of their cotangent line bundles. We will explain the relationship between the two formulas and the Eynard-Orantin topological recursion applied to certain generating series of Hurwitz numbers.