We present some recent results on the asymptotic behavior of almost periodic solutions to stochastic conservation laws and, more generally, degenerate parabolic-hyperbolic equations. Two types if stochastic perturbations are considered: forcing and rough-flux. The part concerning the forcing stochastic source is from joint works with Claudia Espitia and Daniel Marroquin. The part concerning stochastic rough-flux is from a joint project with Rui Jin Yachun Li and João Nariyoshi.