The objective of this article is to define the different stages involved in the 3D reconstruction of arteries and to review, from our experience and from the literature, the solutions already proposed. A full reconstruction framework includes the characterization of the imaging device (in terms of distortion and calibration), the specificity of the image acquisition process, the preprocessing that can be applied, the detection of the vascular structures, the 2D feature formation, the reconstruction itself, and the visualization aspects. They are examined according to a computer vision approach where two or three views are assumed to be available. Their generalization to temporal image sequences are also considered. Some of the material reported here is unpublished. The article allows the reader to identify the true critical issues that are not often clearly mentioned in the literature and the challenges that they convey. A final discussion presents a few perspectives in this area of research.