Efficient data transmission is an important part of satellite communication, particularly when large data volumes need to be downlinked to the Earth. One general approach to dealing with this dilemma is data compression, either lossless or lossy. For hyperspectral data, compression is specifically crucial due to its high inter-band spectral correlation, resulting from the use of hundreds of high spectral resolution bands for data collection. This paper develops a new approach, called progressive band selection (PBS), to achieve both data compression and data transmission, in the sense that data can be compressed and transmitted progressively. First, PBS prioritizes each spectral band by assigning a priority score based on its information content measured by a certain criterion. Then, bands are selected progressively according to the priority scores assigned to each spectral band. Consequently, data can be compressed and transmitted in a progressive fashion to meet the application's requirements; this task cannot be accomplished by most data compression techniques. Most importantly, PBS can be implemented in two opposite manners. One is forward progressive band selection (FPBS), which starts with a low number of bands and gradually improves data quality by including more bands progressively, based on their priority scores, until data quality is satisfactory. The other is backward progressive band selection (BPBS), which begins with a high number of spectral bands and progressively removes them in accordance with their priority scores, until data quality falls below a given tolerance level. In order to determine the lower and upper bounds on the number of bands used for FPBS and BPBS, we use a recently developed concept called virtual dimensionality (VD). We demonstrate the utility of PBS in compression and transmission for satellite communication with an experiment in land use and cover classification, which uses a dataset collected by the Hyperion instrument aboard NASA's EO-1 satellite.