Design optimisation is of paramount importance in most engineering, e.g. aeronautical, automotive, or naval, disciplines. Its interdisciplinary character is manifested in the synthesis of geometric modelling, numerical analysis, mathematical programming, and computer sciences. The evolution of the field is closely related to concomitant advances in these diverse research areas. Historically, there has always been a strong desire to unify these equally important fields of contemporary engineering. However, creating sophisticated computer-aided engineering (CAE) systems that nicely integrate these elements remained a formidable matter thus far. The purpose of this work is to demonstrate that computer-aided geometric design (CAGD), physical analysis, and design optimisation are inherently joint engineering endeavours and maybe beneficially integrated in a common framework. The inspiration of this work emanates from the recently introduced isogeometric analysis. The isogeometric paradigm is aimed at unifying the geometric and analysis descriptions of engineering problems. This unification is brought about by integrating the geometric description of a design and its analysis. Consequently, the isogeometric approach provides a natural environment to develop design optimisation tools. In this dissertation, a comprehensive non-uniform rational B-splines (NURBS) based isogeometric structural design optimisation framework is introduced. The proposed design framework is developed for sizing, form finding, and the coupled optimisation of form and sizing. Salient elements of isogeometric design include distinct interpolation schemes, a multilevel design scheme, the shape change norm, and the variational constraint formulation. Harmony between the different components is emphasized through consistent use of isogeometric concepts and precepts. Owing to the weight-sensitive nature of most aerospace constructions, the primary focus is the design of Cosserat structures, particularly rods and shells of the Kirchhoff-Love class. It is however worth highlighting that the fundamental ideas introduced in this work are applicable to general structural models. The isogeometric design framework is first verified in the context of sizing and form finding of isotropic and elastic planar arches. Subsequently, the more challenging task of thin-walled variable stiffness composite shell optimisation is performed. Here, it is aimed at finding the optimal in-plane material anisotropy distribution as well as the shape. The considered mathematical programming problems are solved by utilising the technique of sequential convex conservative approximations (CCA). While separable CCAs are employed to deal with relatively large-scale structural sizing problems, a non-separable CCAs-based algorithm is developed to solve isogeometric form finding problems. The applicability of the framework is demonstrated using several example problems involving frequently employed design objectives and constraints, e.g. structural weight and stiffness, buckling load factor, fundamental frequency, or strength. The attained numerical results indicate good applicability of the proposed design framework.