We introduce a transfer-function-guided 3D block-based saliency-aware compression scheme for volumetric data that is both content- and spatially-scalable. Salient 3D volumetric blocks are identified and weighted with the help of a transfer function which is used to render the data. We describe our method in the form of a framework for processing, progressive transmission, and visualization of volumetric data on a target device, such as a mobile device with limited computational resources. In particular, we address the transmission bottleneck incurred when transferring 3D volumetric data. Identified salient regions are progressively transmitted to the target device. The received data is rendered progressively in the respective order with a predefined or user-defined transfer function. Our method is developed with medical applications in mind, where preservation of all information is essential for clinical diagnosis. Because our method is integrated into a resolution scalable coding scheme with an integer wavelet transform of the image, it allows the rendering of each significant region at a different resolution up to fully lossless reconstruction. We perform a thorough qualitative and quantitative evaluation of the saliency detection method and the resulting saliency-aware compression schemes. Our results show reduced error in representation of the volumetric data with our method.