Mesh-Free FD Approximations are easy to work with and are in some sense optimal in their representations of functions locally around a single point. However, in more than one dimension, approximations based on polynomial interpolants encounter severe difficulties if the node points are not regularly placed (grid-based). Additional difficulties often arise at boundaries which (above 1-D) may be irregularly shaped, and also from mixtures of scales across a computational domain that may require spatially variable resolution. It transpires that radial basis functions (RBFs) can favorably replace (or supplement) polynomials in such situations. Their use in creating spatially local and highly effective FD-type approximations is quite recent.