Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. Shapes are in fact unparametrized curves, evolving on a vector space, on a Lie group or on a manifold. One popular approach to shape analysis is by the use of the Square Root Velocity Transform (SRVT). In this talk we propose a generalisation of the SRVT from vector spaces to Lie groups and to homogeneous manifolds. This is Joint work with S. Eidnes, A. Schmeding.