In this talk we consider localized solutions of pulse type of reaction-diffusion equations. We briefly discuss the existence and stability of solitary pulses, but our main interest lies in the dynamics of interacting pulses. We introduce the concept of semi-strong pulse interactions, that goes beyond the limitations of the weak interaction case, in which the pulses are assumed to be 'sufficiently far apart'. Unlike in the weak interaction case, semi-strong interacting pulses change in shape and character. We derive equations for the evolution of semi-strong interacting pulses and develop a renormalization group technique to establish the nonlinear asymptotic stability of semi-strong pulse interactions in a Gierer-Meinhardt system.