  We investigate propagating fronts in disordered media that belong to the
universality class of wetting contact lines and planar tensile crack fronts. We
derive from first principles their nonlinear equations of motion, using the
generalized Griffith criterion for crack fronts and three standard mobility
laws for contact lines. Then we study their roughness using the self-consistent
expansion. When neglecting the irreversibility of fracture and wetting
processes, we find a possible dynamic rough phase with a roughness exponent of
$\zeta=1/2$ and a dynamic exponent of z=2. When including the irreversibility,
we conclude that the front propagation can become history dependent, and thus
we consider the value $\zeta=1/2$ as a lower bound for the roughness exponent.
Interestingly, for propagating contact line in wetting, where irreversibility
is weaker than in fracture, the experimental results are close to 0.5, while
for fracture the reported values of 0.55--0.65 are higher.
