Whilst atom probe tomography (APT) is a powerful technique with the capacity to gather information containing hundreds of millions of atoms from a single specimen, the ability to effectively use this information creates significant challenges. The main technological bottleneck lies in handling the extremely large amounts of data on spatial-chemical correlations, as well as developing new quantitative computational foundations for image reconstruction that target critical and transformative problems in materials science. The power to explore materials at the atomic scale with the extraordinary level of sensitivity of detection offered by atom probe tomography has not been not fully harnessed due to the challenges of dealing with missing, sparse and often noisy data. Hence there is a profound need to couple the analytical tools to deal with the data challenges with the experimental issues associated with this instrument. In this paper we provide a summary of some key issues associated with the challenges, and solutions to extract or "mine" fundamental materials science information from that data. (C) 2015 Published by Elsevier B.V.