This lecture is devoted to the presentation of two particular "hierarchical" approaches to numerical shape optimization in aerodynamics design: 1) multilevel parametric shape optimization algorithms; 2) additive preconditioners. The first approach is inspired from the classical geometrical multigrid method, except that here the geometrical levels are associated with embeded Bezier parametrizations of different degrees of a shape subject to optimization, and in general only one (fine) grid is used to solve the flow equations (Euler equations of compressible gas dynamics). The second approach uses the framework of a descent method in which the gradient with respect to the nodal coordinates is computed by using an adjoint solver. The flow is computed by finite volumes and agglomeration multigrid. The hierarchy of agglomerated grids is employed to construct an additive preconditioner inspired from the Bramble-Pasciak-Xu regularization.