The ideal picture of a near-perfect 3D microscope often presented regarding Atom Probe Tomography faces several issues. These issues degrade the metrological performance of the instrument and find their roots in the phenomena acting at the atomic to the mesoscopic level in the vicinity of the surface of a field emitter. From the field evaporation process at the atomic scale, to the macroscopic scale of the instrument, the path to model the imaging process and to develop more accurate and reliable reconstruction algorithms is not a single lane road. This paper focused on the numerical methods used to understand, treat, and potentially heal imaging issues commonly affecting the data in atom probe experiments. A lot of room for improvement exists in solving accuracy problems observed in complex materials by means of purely electrostatic models describing the image formation in a classical approach. Looking at the sample at the atomic scale, the phenomena perturbing the imaging process are subtle. An examination of atomic scale modifications of the sample surface in the presence of a high surface electric field is therefore mandatory. Atomic scale molecular dynamic models integrating the influence of the high surface electric are being developed with this aim. It is also demonstrated that the complex behavior of atoms and molecules in high fields, and consequences on collected data, can be understood through the use of accurate ab-initio models modified to include the impact of the extreme surface electric field.