Linear connections with torsion in semi-Riemannian varieties are a generalisation of the Levi-Civita connection. They appear naturally when the manifold is endowed with additional geometric structures and look for metric connections which also parallelise these additional structures. Remarkable examples of this situation are reductive homogeneous spaces, nearly-Kähler varieties, Sasakian structures, etc. Cartan geometries of type (G,H) on a manifold M, where G is a Lie group and H a closed subgroup of G, allow one to construct geometric structures similar to those of the homogeneous space G/H on the manifold M. These geometries allow one to view the manifold M as a curved analogue to the model space G/H, which in this context can be thought of as the flat model of the structure. Cartan geometries allow to give uniform constructions for very different types of geometries such as semi-Riemannian geometries, conformal geometry or projective differential geometry, etc.