This chapter presents a streamlined introduction to rigidity theory for bar-joint frameworks in Rd $ \mathbb R^d $ where the underlying metric is governed by a polyhedral norm (as opposed to the Euclidean norm). Non-Euclidean rigidity theory, in which an alternative metric or quadratic form is used to set geometric constraints, appears to be a relatively new topic. It has been considered by various authors in the contexts of spherical and hyperbolic geometry and in pseudo-Euclidean spaces. One benefit of working in this setting is that we retain much of the interplay between real analysis and linear algebra that underpins Euclidean rigidity theory. Rigidity can sometimes be detected by simple path chasing argument. For frameworks with a non-trivial symmetry group, rigidity may also be detected by considering monochrome subgraph decompositions in an associated gain graph (G0,ψ) $ (G_0,\psi ) $.