Isogeometric Analysis (IGA) offers high-order accuracy and exact geometry representation by employing spline spaces defined on a parametric domain and mapped to the physical domain through a geometry transformation. Refinement can be performed independently in each parametric direction, making IGA a natural framework for anisotropic mesh refinement [3]. However, whether this anisotropy is effectively transferred to the physical domain strongly depends on the chosen geometry parameterization; for instance, polar transformations do not preserve mesh size ratios between parametric and physical space [1,2]. The choice and construction of suitable isogeometric parameterizations are particularly challenging in the presence of non-smooth geometric features. In this contribution, we review the state of the art in anisotropic mesh refinement for IGA and discuss representative applications, while also investigating in more detail the influence of the geometry mapping on the relation between parametric and physical anisotropy.