Abstract: This paper summarizedthe recent progress in the symmetries and conserved quantities ofclassical constrained mechanical systems. The five stages ofclassical mechanics are introduced and the three problems areproposed. The Noether symmetry, the Lie symmetry, the forminvariance, the symmetry of Lagrangians, the conformal invarianceand the conserved quantities of the systems are dsicussed, andsome future research problems are proposed.