The last 15 years were marked with substantial progress in constrained optimization due to the well known developments in the Interior Point Methods (IPM). We will discuss an alternative to the IPM approach to constrained optimization based on the Nonlinear Rescaling principle. The NR approach consists of rescaling the objective function and/or the constraints of a given constrained optimization problem into an equivalent one and using the Lagrangian for the equivalent problem for both theoretical analysis and numerical methods. The NR method alternates unconstrained minimization of the Lagrangian for the equivalent problem in primal space with both the Lagrange multipliers and scaling parameters update. Our main concentration is the Primal-Dual NR (PDNR) method. It replaces the NR step by solving a particular Primal-Dual (PD) system of equations. Application of the Newton method to PD system leads to the PDNR method that for convex optimization converges under minimum assumptions on the input data. We will show that under the standard second order optimality condition it converges with QUADRATIC rate. Application of the PDNR for solving large scale real life constrained optimization problems and correspondent numerical results will be discussed.