In high-contrast composite materials, the stress concentration is a common phenomenon when inclusions are close to touch. It always causes damage initiation. This problem was proposed mathematically by Ivo Babuska, concerning the system of linear elasticity, modeled by a class of second order elliptic systems of divergence form with discontinuous coefficients.  I will first review some of our results on upper bound estimates by developing an iteration technique with respect to the energy integral to overcome the difficulty from the lack of maximal principle for elliptic systems, then present two very recent results of myself on lower bound estimates and asymptotics of the gradients to show that the blow-up rates are actually optimal in dimensions two and three. Finally, I will show that our framework can be applied to investigate the corresponding concentration phenomenon for p-Lapalacian, Fishler Lapalacian in Finsler geometry, and suspension problems in some fluid-solid model in Stokes equation setting.