  In this review we present an overview of the current atom probe tomography
spatial data reconstruction paradigm, and explore some of 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.
