I shall give an overview of Hamilton-Jacobi and reaction-diffusion fronts in stationary ergodic random flows in terms of stochastic homogenization and the variational formula of front speeds of the Kolmogorov-Petrovsky-Piskunov (KPP) reactions. Large deviation property of the random flows is essential to the formula and the analysis of front speed asymptotics. The variational formula also leads to a computational method on random KPP front speeds.