This paper aims to present an overview on the influence of rheological heterogeneity and mechanical anisotropy on the deformation of continents. After briefly recapping the concept of rheological stratification of the lithosphere, we discuss two specific issues: (1) as supported by a growing body of geophysical and geological observations, crust=mantle mechanical coupling is usually efficient, especially beneath major transcurrent faults which probably crosscut the lithosphere and root within the sublithospheric mantle; and (2) in most geodynamic environments, mechanical properties of the mantle govern the tectonic behaviour of the lithosphere. Lateral rheological heterogeneity of the continental lithosphere may result from various sources, with variations in geothermal gradient being the principal one. The oldest domains of continents, the cratonic nuclei, are characterized by a relatively cold, thick, and consequently stiff lithosphere. On the other hand, rifting may also modify the thermal structure of the lithosphere. Depending on the relative stretching of the crust and upper mantle, a stiff or a weak heterogeneity may develop. Observations from rift domains suggest that rifting usually results in a larger thinning of the lithospheric mantle than of the crust, and therefore tends to generate a weak heterogeneity. Numerical models show that during continental collision, the presence of both stiff and weak rheological heterogeneities significantly influences the large-scale deformation of the continental lithosphere. They especially favour the development of lithospheric-scale strike-slip faults, which allow strain to be transferred between the heterogeneities. An heterogeneous strain partition occurs: cratons largely escape deformation, and strain tends to localize within or at the boundary of the rift basins provided compressional deformation starts before the thermal heterogeneity induced by rifting are compensated. Seismic and electrical conductivity anisotropies consistently point towards the existence of a coherent fabric in the lithospheric mantle beneath continental domains. Analysis of naturally deformed peridotites, experimental deformations and numerical simulations suggest that this fabric is developed during orogenic events and subsequently frozen in the lithospheric mantle. Because the mechanical properties of single-crystal olivine are anisotropic, i.e. dependent on the orientation of the applied forces relative to the dominant slip systems, a pervasive fabric frozen in the mantle may induce a significant mechanical anisotropy of the whole lithospheric mantle. It is suggested that this mechanical anisotropy is the source of the so-called tectonic inheritance, i.e. the systematic reactivation of ancient tectonic directions; it may especially explain preferential rift propagation and continental break-up along pre-existing orogenic belts. Thus, the deformation of continents during orogenic events results from a trade-off between tectonic forces applied at plate boundaries, plate geometry, and the intrinsic properties (rheological heterogeneity and mechanical anisotropy) of the continental plates.