  Self-sustained reaction fronts in a disordered medium subject to an external
flow display self-affine roughening, pinning and depinning transitions. We
measure spatial and temporal fluctuations of the front in $1+1$ dimensions,
controlled by a single parameter, the mean flow velocity. Three distinct
universality classes are observed, consistent with the Kardar-Parisi-Zhang
(KPZ) class for fast advancing or receding fronts, the quenched KPZ class
(positive-qKPZ) when the mean flow approximately cancels the reaction rate, and
the negative-qKPZ class for slowly receding fronts. Both quenched KPZ classes
exhibit distinct depinning transitions, in agreement with the theory.
