in this talk, i will describe my results on superconvergence estimates of mixed methods using raviart--thomas finite elements. first i prove the canonical interpolant and finite element solution approximating the vector variable are superclose in $l^2$ norm. the main tool is a triangular integral identity in bank and xu siam j. numer. anal 41 (2003) 2294-2312, and a discrete helmholtz decomposition. comparing to previous supercloseness results (eg. brandts numer. math. 68 (1994) 311--324), my proof is constructive and works on irregular triangular meshes. even on a special uniform grid, my result shows that the previous supercloseness result is suboptimal. next i will describe several postprocessing operators based on simple edge averaging, $l^2$ projection or superconvergence patch recovery. then i will show the postprocessed finite element solution superconverges to the true solution. if time permits, i will also briefly describe applications to maxwell's equations an d generalizations to fourth order elliptic equations.