Certain diseases cause permanent changes to the shapes and densities of nailfold capillaries and, therefore, nailfold capillaroscopy is important as a tool for diagnosing and monitoring these diseases. The first aim of the project is to resolve differences in terminology that have developed over the years in previous work. We propose a taxonomy for nailfold capillaries that cover six descriptive classes: cuticulis, open, tortuous, crossed, bushy, and bizarre. The first three are parametric in that they may be distinguished by the ratio of capillary length to width and by the curvature of the capillary limbs. The last three are characterized by their topology; a crossed capillary has a closed area that is not connected to the image background. Bushy and bizarre capillaries have atypical shapes that are characterized by the convex hull of their skeleton. These descriptive classes may be modified according to anomalies in width and length.