In this talk, we consider the gradient blowups from smooth and shock-free (contact discontinuities are included) initial data for the 1D compressible Euler equations and other systems of conservation laws with arbitrarily large initial data. By constructing “decoupled” Riccati equations for gradient variables and defining the compressive and rarefactive characters, we provide a couple of singularity formation results with large data, including a generalization of Lax's results for systems with two unknowns in 1964 to full Euler equations. We also give several exact non-isentropic shock-free solutions. Some works in this talk are collaboration works with Robin Young.