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We compare different scenarios for dendritic melting of alloys with respect to the front propagation velocity. In contrast to conventional dendritic growth, selection can here be also due to the presence of a grain boundary or coherency strains, and the propagation speed is higher. The most favorable situation is partial melting, where two parabolic fronts, one melting and one solidifying interface, are moving together, since the process is then determined by diffusion in the thin liquid layer. There, and also in phase field simulations of melting in peritectic and eutectic systems, we observe a rotation of the triple junction relative to the growth direction. Finally, we discuss the role of elastic effects due to density and structural differences on solid-state phase transformations, and we find that they significantly alter the selection principles. In particular, we obtain free dendritic growth even with isotropic surface tension. This is investigated by Green's function methods and a phase field approach for growth in a channel, and illustrated for the formation of a twin phase.