Solutions of the mathematical models well simulate real-life physical behavior of the physical problems. So, and with the development of computer algebraic systems, many analytical and numerical techniques for obtaining the target solutions have taken a lot of interest. The book includes a detailed investigation of two recently developed analytical methods that show potential in solving nonlinear equations of various kinds (differential, integral, integro-differential, difference-differential) without discretizing the equations or approximating the operators. The considered methods are mainly the homotopy perturbation method (HPM) and the variational iteration method (VIM). In this work, basic ideas of the HPM and VIM are illustrated; convergence theorems of the considered methods for various types of equations are proved; modifications and treatments in HPM and VIM are done; test examples for further illustration of the methods are solved; many applications in fluid mechanics and physics fields are investigated using modified techniques; and finally, all obtained results are verified through the comparison with exact/numerical solutions or previously published results.