A gradient-based shape optimization methodology based on continuous adjoint sensitivities has been developed for two-dimensional steady Euler equations on unstructured meshes and the unsteady transonic small disturbance equation. The continuous adjoint sensitivities of the Helmholtz equation for acoustic applications have also been derived and discussed. The highlights of the developments for the steady two-dimensional Euler equations are: i) generalization of the airfoil surface boundary condition of the adjoint system to allow for proper closure of the Lagrangian functional associated with a general cost functional and ii) transformation to the natural coordinates alongside with the restriction of the domain state equation to the boundary to rid the sensitivity integrals from non-tangential derivative terms in order to overcome the Babuska paradox. With regard to the unsteady transonic small disturbance equation (UTSD), the continuous adjoint methodology has been successfully extended to unsteady flows. It has been demonstrated that for periodic airfoil oscillations leading to limit-cycle behavior, the Lagrangian functional can be only closed if the time interval of interest spans one or more periods of the flow oscillations after the limit-cycle has been attained. Unlike the Euler equation sensitivities, the Helmholtz equation requires the Hessian of the acoustic field on the control surface as well. Again, it has been shown that in the natural coordinates, the only required derivative information are the first and second order tangential derivatives of the acoustic field. If it were to be attempted, the sensitivities of the Navier-Stokes equations would also require the Hessian of the state variables. Based on above experiences, it is contended that a transformation to the trihedral coordinate system may ease the problem associated with the acquisition of accurate boundary derivative information.