The test ideal is an invariant which measures singularities in positive characteristic commutative algebra. While appearing first in the celebrated theory of tight closure due to Hochster and Huneke, the importance test ideal in algebraic geometry is due to its mysterious correspondence with the multiplier ideal after reduction to characteristic $p >> 0$. I will report on recent joint work with Karl Schwede on the behavior of the test ideal under separable finite morphisms. The trace map plays a central role in our analysis, and also allows us to show an algebraic result of independent interest on the lifting properties of $p^{-e}-linear$ maps.