Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t)~tdl, where dl is the connectivity dimension. In a percolating channel, a statistically stationary traveling wave develops. The speed and the width of the traveling wave are numerically computed.