In this work we present a fully integrated framework for aerodynamic shape optimisation. In order to develop an efficient design chain, a high level of automation is required. To this end, we propose an isogeometric approach, in which the same mathematical representation is adopted for the shape to optimize, the computational domain and the physical solution, without any geometrical approximation. It results in a tight coupling between the Computer Aided Design (CAD) tool, the mesh generation / adaption and the Computational Fluid Dynamics (CFD) solver. As a consequence, all transfers of information between the components of the design loop are significantly facilitated. The compressible Navier-Stokes equations are solved using the Isogeometric Discontinuous Galerkin scheme. The flow solver is then coupled with an Efficient Global Optimisation (EGO) algorithm to complete the design chain. We first demonstrate the capability of the developed methodology by considering a classic drag reduction problem, in which an airfoil shape is optimised for a transonic flow condition. Since the position of the shock on the airfoil surface is a function of the geometry, traditional approaches require highly refined meshes in a large area to properly capture the discontinuity for all the possible designs. However, thanks to the isogeometric formulation, we can exploit an Adaptive Mesh Refinement technique presented to further reduce the computational costs by refining locally the mesh while preserving exactly the geometry. As a second test case, we study an active morphing technique to control the boundary layer separation over an airfoil. The Arbitrary Lagrangian-Eulerian approach proposed is used for solving the flow equations on the time-dependent deforming domain. The isogeometric methodology allows an accurate description and a control of the regularity of the deformation of the airfoil surface. The EGO algorithm is thus used to find the optimal set of parameters for the morphing technique.