In scientific and engineering computing, one major computational bottleneck is the solution of large scale linear algebraic systems resulted from the discretization of various partial differential equations (PDEs). These systems are still often solved by traditional methods such as Gaussian elimination in many practical applications. Mathematically optimal methods, such as multigrid methods, have been developed for decades but they are still not much used in practice. In this talk, I will report some recent advances in the development of optimal multilevel iterative methods that can be applied to various practical problems in a user-friendly fashion. Starting from some basic ideas of designing efficient iterative methods such as multigrid and domain decomposition methods, I will give a brief description of a general framework known as the Fast Auxiliary Space Preconditioning (FASP) Methods and report some applications in various problems including Newtonian and non-Newtonian models, Maxwell equations, Magnetohydrodymics and battery and reservoir (porous media) simulations.