Registration means to bring two or more shapes into a suitable relative configuration (position and orientation). In its major applications like 3D scan alignment, the aim is to coalesce data and regions originating from the same physical region have similar local form. So, the correspondence between shapes is discoverable from the shapes themselves, and the registration makes corresponding regions coincide. This work concerns the registration of shapes to satisfy a purpose or intent, not involving data integration. Regions relevant to the purpose are marked as patches correspondingly on two input 3D meshes of objects. Then, a method of registration is used to obtain the suitable configuration. Three methods of registration are explored in the present work. The first method of registration is to align intrinsic co-ordinate frames defined on the shapes. This is used in a scenario of comparison of shapes with dissimilar local form, which are to be aligned as an expert requires, as in the comparison of dental casts and apple bitemarks in forensics. Regions recognized in dentistry are marked as patches on the cast and bitemark shapes by a dentist. From these, an intrinsic frame is defined and aligned to bring the shapes close. The alignment is used to calculate distortion of a deteriorated bitemark. Another application of frame alignment is the analysis of shape variation of contours in a population for wearable product design. A frame based on anthropometric landmarks is used to construct the contours of the product's interface with the body-part, analyze its spread through a 2D grid-statistics method, and construct the interface shape. The frame helps assess the fit of the constructed shape on an individual. The method is demonstrated with respirator masks. Frame-based alignment is seen to give unsatisfactory results with head shapes for motorcycle-helmet interior design, as it does not adequately describe the helmet-head interaction. This inspires the second method of registration. The second method of registration is the biased minimization of distance between corresponding patches on the shapes, by weighting patches to indicate their importance in the registration. The method is used to assess the small deviation of precisely-known quantities in shapes, such as in manufactured part inspection. Here, the patches marked are grouped, and the part and model shapes registered at patches in the combinations of groups, by giving a binary weighting of 1 to these patches and 0 to others. The deviation of every patch across the registrations at multiple datum systems is tabulated and analyzed to infer errors. The method is exemplified with welded bars and bent-pipes. In the analysis of head-shape variation in a population to create headforms for wearable products, the deviations are large and not precisely known. So, the head shapes are registered at patches on regions pertinent to the product's functioning, with a relatively higher weight for a reference patch. A 3D grid-statistics method is used to analyze the shapes' spread and arrive at the headform shapes. The selection of head form for a given head shape is also treated. The method is demonstrated with motorcycle helmets and respirator masks. Biased distance-minimization is applied to obtain the mechanical assembly of part meshes. Different schemes of marking patches are tested as cases. The method leads to both intended and unintended final configurations, prompting for a better objective in registration. Thus, the third method of registration, that of normals is proposed; this happens in a transformed space. By analyzing the nature of assembly in CAD systems, the face-normals of the mesh are used to obtain the intended orientation of parts. The normals of corresponding patches are registered using three methods of registration, namely on a unit-sphere, of unit-normals, and spherical co-ordinates of normals. In each method, the optimal transformation is suitably converted to be applied on the actual part shape in 3D. Unit-normal alignment gives sensible results, while the other two lead to skewed final orientations. This is attributed to the nature of the space of registration. The methods are applied to examples involving different assembly relations, such as alignment of holes. On the whole, it is shown that correspondence embodies the knowledge of importance of regions on shapes for a purpose. The registration method should lead to an apt shape placement, which need not always mean coincidence. In essence, correspondence denotes 'what' regions are of relevance, and registration, 'how' to get the relative configuration satisfying a purpose or intent.