The study of the structure and function of neuronal cells and networks is of crucial importance in the endeavor to understand how the brain works. A key component in this process is the extraction of neuronal morphology from microscopic imaging data. In the past four decades, many computational methods and tools have been developed for digital reconstruction of neurons from images, with limited success. As witnessed by the growing body of literature on the subject, as well as the organization of challenging competitions in the field, the quest for a robust and fully automated system of more general applicability still continues. The aim of this work, is to contribute by surveying recent developments in the field for anyone interested in taking up the challenge. Relevant aspects discussed in the article include proposed image segmentation methods, quantitative measures of neuronal morphology, currently available software tools for various related purposes, and morphology databases. (c) 2010 International Society for Advancement of Cytometry.