We will discuss a generalized mean curvature flow and relation with the isoperimetric problems. A locally constrained mean curvature flow was introduced by Junfang Li and myself in space forms, Guan-Li-Wang extended the flow to general warped product spaces afterwards. The flow served as a path to the optimal solution to the isoperimetric problem in these spaces. Very recently, the flow was further generalized to Riemannian manifolds admitting conformal Killing fields by works of Li-Pan and Flynn-Reznikov. The recent results illustrate the intimate relationship of problems in calculus of variations and geometric flows. We will also discuss some open problems in this direction.