In this review we present an overview of the current atom probe tomography spatial data reconstruction paradigm, and explore some potential routes to improve the current methodology in order to yield a more accurate representation of nanoscale microstructure. Many of these potential improvement methods are directly tied to extensive application of advanced numerical methods, which are also very briefly reviewed. We have described effects resulting from the application of the standard model and then introduced several potential improvements, first in the far field, and, second, in the near field. The issues encountered in both cases are quite different but ultimately they combine to determine the spatial resolution of the technique.