We present a theoretical study of polymer-polymer reaction kinetics at an interface separating two immiscible polymer phases. Such reactions are widely employed in reactive blending of incompatible species. When functional groups are weakly reactive, the rate constant it obeys mean field theory : k proportional to h, where h is the interface thickness. For strongly reactive end groups (diffusion-controlled limit) we show that the interface increases the effective dimensionality of the problem by one : reaction rates obey scaling laws as for a 4-dimensional bulk problem. This leads to k similar to 1/ln N and k similar to 1/N (to within logarithmic factors) for unentangled and entangled melts, respectively, where N is the degree of polymerization. These are quite different from the corresponding scalings for bulk reactions : k similar to 1/N-1/2 and k similar to 1/N-3/2. k depends only logarithmically on h for unentangled systems and is independent of h for entangled cases. As the interface becomes crowded with diblock product, k becomes exponentially small when the area per chain, Sigma, drops below N-1/2 : k similar to, e(-const N/Sigma 2). Consistent with a number of experiments, we conclude that during reactive blending surface tension reduction is minimal and reduced droplet-droplet coalescence rates are dominant.