For an efficient engineering design process, a seamless integration of computer aided design (CAD) and numerical analysis is crucial. Various numerical methods are used in engineering analysis, among which the finite element method (FEM) is the most prominent. This method relies heavily on a mesh structure, and the generation of this mesh generation accounts for about 80% of a typical analysis time for practical engineering problems. Various ideas have been proposed in the literature to avoid these problems by either simplifying this mesh generation process, or relaxing some of the constraints associated with the very presence of a mesh. This talk aims to present an overview of the recent advances in this direction of the most versatile and prominent approaches to overcome the mesh burden in computational science, namely: (a) Iso-geometric analysis whose focus is to closely tie the geometry, i.e. CAD data to the analysis; (b) the extended/generalized FEM (X/GFEM) where one of the aims is to increase the independence between the problem solved and the mesh. These methods are particularly attractive as they afford the modelling of crack propagation without re-meshing. Inclusions and holes as well as the domain boundary can also be treated independently of the mesh; (c) Strain smoothing in finite elements allows decreasing the negative effects of mesh distortion, (d) polygonal finite element method where the constraint on the mesh topology is relaxed and (e) scaled boundary finite element method - a semi-analytical method.