This work explores the full potential of isogeometric shape functions for global digital image correlation. To this end, a novel DIC and DHC (digital height correlation) methodology have been developed based on adaptive refinement of isogeometric shape functions. Non-Uniform Rational B-Spline (NURBS) shape functions are used employed of their flexibility and versatility, which enables a wide range of kinematic descriptions. In the adaptive refinement algorithm, the shape functions are automatically adjusted to be able to describe the kinematics of the sought (2D or 3D) displacement field with an optimized number of degrees of freedom. Both methods show high accuracy as demonstrated by various virtual experiments with predefined, highly localized (2D and 3D) displacement field. For adaptive iso-GDIC, real tensile tests of complex sample geometries demonstrate its effectiveness in practice, showing local refinement at the areas of localization, without the need of making problem-specific choices regarding the structure of the shape functions. For adaptive iso-GDHC, the correlation of surface height profiles of deforming stretchable electronics structures shows successful autonomous refinement at two localized buckles, thereby strongly reducing the 3D residual, while also analytical differentiation of the C1-continuous 3D displacement field yields the curvature field of the deforming stretchable interconnect.