Regularity results for strongly nonlinear elliptic and parabolic systems

We consider elliptic and parabolic systems of equations with strong (quadratic) nonlinearity in the gradient. We discuss the known partial regularity results and the author’s results of the last years.
Assuming a one-side restriction on the strongly nonlinear term, we describe conditions that guarantee local smoothness of weak possibly unbounded solutions of quasilinear and nonlinear systems.