Tight closure has shaped the way commutative algebraists study singularities in rings of positive characteristic. There have been a number of attempts to define a comparable closure operation in the equal characteristic 0 setting, but up until now most of them have been defined using reduction to positive characteristic. In this talk I will define several closure operations using characteristic 0 structures that detect KLT or rational singularities. This work is joint with Neil Epstein, Peter McDonald, and Karl Schwede.