  Barbour's interpretation of Mach's principle led him to postulate that
gravity should be formulated as a dynamical theory of spatial conformal
geometry, or in his terminology, "shapes." Recently, it was shown that the
dynamics of General Relativity can indeed be formulated as the dynamics of
shapes. This new Shape Dynamics theory, unlike earlier proposals by Barbour and
his collaborators, implements local spatial conformal invariance as a gauge
symmetry that replaces refoliation invariance in General Relativity. It is the
purpose of this paper to answer frequent questions about (new) Shape Dynamics,
such as its relation to Poincar\'e invariance, General Relativity, Constant
Mean (extrinsic) Curvature gauge, earlier Shape Dynamics, and finally the
conformal approach to the initial value problem of General Relativity. Some of
these relations can be clarified by considering a simple model: free
electrodynamics and its dual shift symmetric formulation. This model also
serves as an example where symmetry trading is used for usual gauge theories.
