In this talk, I will focus on the connection between two important measures of singularities: multiplier ideals in characteristic zero and test ideals in positive characteristic. While their relationship is well understood in many cases (e.g. hypersurface or finite quotient singularities), it remains conjectural for non-\mathbb{Q}-Gorenstein varieties (such as the cone over the Segre embedding of \mathbb{P}^1 \times \mathbb{P}^2 in \mathbb{P}^5). I will discuss positive recent progress on this conjecture for so-called numerically \mathbb{Q}-Gorenstein varieties (which include all normal surface singularities). This is joint work with T. de Fernex, R. Do Campo, and S. Takagi.