This thesis contains 8 manuscripts for peer-reviewed journals (4 published, 2 submitted, 2 to be submitted within 4 weeks) that present studies of deformation microstructures and folds in polar ice and ductile anisotropic rocks by means of numerical simulations. It is organized in four different parts that focus: (1) Viscoplastic deformation of polycrystalline polar ice in simple and pure shear coupled with dynamic recrystallisation simulating microstructure evolution and formation of folds; (2) Folding and unfolding of single and multilayers in pure and simple shear; (3) Influence of anisotropy degree and type on rotation of rigid bodies (porphyroclasts and porphyroblasts); and (4) Analysis of the effects of dynamic recrystallisation on the rheology and microstructures of partially molten rocks. The first part (chapters 2, 3 and 4) contains three manuscripts analysing the influence of dynamic recrystallisation on deformation of pure polar ice. A full-field viscoplastic code (FFT) that fully reproduces the ice crystal’s mechanical anisotropy is coupled with dynamic recrystallisation processes to perform a series of numerical simulations in pure (chapter 2) and in simple shear (chapter 3 and 4). The results show that dynamic recrystallisation (DRX) has remarkable effects on the developed ice microstructures, producing larger and more equidimensional grains and masking strain heterogeneities. DRX has only a minor effect on the formation of lattice preferred orientations (LPOs), but it has a strong influence on the relative activity of the different slip systems of ice and, therefore, on its mechanical properties. The survival probability of ice grains during recrystallisation is mostly related to the initial grain size, while crystal orientation with respect to the deformation axes plays a minor role only. The last manuscript of this part analyses how folds form in polar ice (chapter 4) as a consequence of intrinsic anisotropy when a strong LPO has developed. This mechanism can explain the development of folds in ice, without needing to invoke unrealistic viscosity contrasts between folding layers. The second part of the thesis includes three manuscripts dedicated to the formation of folds in layered composite materials. The first of these manuscripts (chapter 5) investigates the development of folding of a single layer embedded in a softer matrix in linear and non-linear viscous media. Viscous deformation is simulated using a finite-element method (FEM) up to high strains. This study focuses on the influence of viscosity contrast, vorticity of deformation and the stress exponent on the resulting folding geometries. Folds forming in pure and simple shear do not develop distinctly different geometries, and are thus difficult to distinguish in the field. Folds formed under non-coaxial flow are slightly more irregular with more variable axial plane orientations than in pure shear. This study demonstrates that the best tool to distinguish simple shear folds is the asymmetry of associated axial plane cleavage. Chapter (6) presents an analysis of the instantaneous stress and strain fields of the simulations studied in the previous chapter to compare the mechanical behaviour of folding rocks under pure and simple shear. Most notably, the work required to fold a competent layer is lower in simple shear than in pure shear. Chapter 7 studies the response of a folded layer that goes into the extensional field with progressive non-coaxial deformation. This contribution contains observations and evidence that help to recognise in the field whether straight layers have been folded previously. Intrafolial and cusp-like folds adjacent to straight layers are indications of previous folding if layers experienced softening during or before stretching, or if the layers were influenced by adjacent layers with different rheologies. The third part of the thesis includes one manuscript (chapter 8) that addresses how the degree and type of anisotropy influence the rotation of rigid bodies embedded in a softer matrix (porphyroclasts and porphyroblasts) under non-coaxial flow. Viscoplastic full field numerical simulations were used to analyse systems with intrinsic anisotropies, and linear viscous FEM for the modelling of systems with composite anisotropies. The results demonstrate that a high degree of anisotropy can slow down or block the rotation of rigid objects. It thus reconciles the opposing positions in the decade-long controversy regarding the rotation of rigid objects, such as garnets, in rocks. The final part of this thesis (chapter 9) investigates the effect of viscosity contrast, linear viscous rheology, melt fraction and wetting angle on the effective weakening of rocks with melt pockets and polar ice with air bubbles. This study is based on the coupling of a linear viscous FEM with dynamic recrystallisation, simulating the evolution in simple shear of a composite based on a foam texture. The results indicate that dynamic recrystallisation and wetting angles have a first-order impact on the deformation of the aggregate, controlling the connection of melt pockets and bulk mechanical behaviour of the rock. Summarising, this thesis contains a number of studies that highlight how numerical simulations can give insight in structural and mechanical developments in ice and rocks, enabling better interpretation of the observed structures.