Abstract: Nowadays the optimization problems emerging from some application areas such as machine learning and data science are typically huge-scale. They have brought tremendous challenge to the traditional first- and second-order methods. Motivated by this, we study randomized block first- and second-order methods for solving a broad class of nonlinear programming problems, whose computational cost per iteration is typically much lower than that of the full-dimensional ones. We analyze their global convergence and also iteration complexity for finding an approximate solution. We also present some computational results to demonstrate their performance.