Truly hierarchical three-dimensional model coding (3DMC) techniques based on subdivision surfaces have, over merely progressive ones, the advantage of yielding pyramidally nested meshes that inherently approximate the surface of a three-dimensional (3-D) object at increasing levels of detail (LODs). Such a nesting makes it natural to edit (hence animate) the model at different LODs. From a compression efficiency viewpoint, it is also the most advantageous, because it permits us to group into hierarchical sets the 3-D details needed to reposition the new vertices predicted along the subdivision process. We first review extensively previous work on both progressive and hierarchical 3DMC. We then describe our hierarchical 3DMC technique based on subdivision surfaces, which is inspired by the set partitioning in hierarchical trees (SPIHT) coding scheme and has in turn inspired the wavelet subdivision surfaces tool of MPEG-4's Animation Framework eXtension (AFX). We finally compare our technique with several others.