<p style='text-indent:20px;'>The paper surveys, classifies and investigates theoretically and numerically main classes of line search methods for unconstrained optimization. Quasi-Newton (QN) and conjugate gradient (CG) methods are considered as representative classes of effective numerical methods for solving large-scale unconstrained optimization problems. In this paper, we investigate, classify and compare main QN and CG methods to present a global overview of scientific advances in this field. Some of the most recent trends in this field are presented. A number of numerical experiments is performed with the aim to give an experimental and natural answer regarding the numerical one another comparison of different QN and CG methods.</p>