This paper presents an overview on the state-of-the-art in the field of medical image coding. After a summary of the more representative 2D and 3D compression algorithms, a versatile model-based coding scheme for threedimensional medical data is introduced. The potential of the proposed system is in the fact that it copes with many of the requirements characteristic of the medical imaging field without sacrificing compression efficiency. Among the most interesting features are progressively refinable up-to-lossless quality of the decoded information, object-based functionalities and the possibility to decode a single 2D image of the dataset. Furthermore, such features can be combined enabling a swift access to any two-dimensional object of any image of interest with refinable quality. The price to pay is a slight degradation of the compression performance. Though, the possibility to focus the decoding process on a specific region of a certain 2D image allows a very efficient access to the information of interest, which can be recovered to the desired up-to lossless quality. This is believed to be an important feature for a coding system meant to be used for medical applications, which largely compensates for the eventual loss in compression that could be implied.