Neuronal morphology is a fundamental factor influencing information processing within neurons and networks. Dendritic morphology in particular can widely vary among cell classes, brain regions, and animal species. Thus, accurate quantitative descriptions allowing classification of large sets of neurons is essential for their structural and functional characterization. Current robust and unbiased computational methods that characterize groups of neurons are scarce. In this work, we introduce a novel technique to study dendritic morphology, complementing and advancing many of the existing techniques. Our approach is to conceptualize the notion of a Sholl descriptor and associate, for each morphological feature, and to each neuron, a function of the radial distance from the soma, taking values in a metric space. Functional distances give rise to pseudo-metrics on sets of neurons which are then used to perform the two distinct tasks of clustering and classification. To illustrate the use of Sholl descriptors, four datasets were retrieved from the large public repository https://neuromorpho.org/ comprising neuronal reconstructions from different species and brain regions. Sholl descriptors were subsequently computed, and standard clustering methods enhanced with detection and metric learning algorithms were then used to objectively cluster and classify each dataset. Importantly, our descriptors outperformed conventional morphometric techniques (L-Measure metrics) in several of the tested datasets. Therefore, we offer a novel and effective approach to the analysis of diverse neuronal cell types, and provide a toolkit for researchers to cluster and classify neurons.