Several techniques based on the three-dimensional (3-D) discrete cosine transform (DCT) have been proposed for volumetric data coding. These techniques fail to provide lossless coding coupled with quality and resolution scalability, which is a significant drawback for medical applications. This paper gives an overview of several state-of-the-art 3-D wavelet coders that do meet these requirements and proposes new compression methods exploiting the quadtree and block-based coding concepts, layered zero-coding principles, and context-based arithmetic coding. Additionally, a new 3-D DCT-based coding scheme is designed and used for benchmarking. The proposed wavelet-based coding algorithms produce embedded data streams that can be decoded up to the lossless level and support the desired set of functionality constraints. Moreover, objective and subjective quality evaluation on various medical volumetric datasets shows that the proposed algorithms provide competitive lossy and lossless compression results when compared with the state-of-the-art.