Processing enormous hyperspectral data results in high computational complexity. Band selection (BS) is one common practice to accomplish this goal. However, determining the number of bands to be selected and finding appropriate bands for BS are very challenging since it requires an exhaustive search. Instead of directly dealing with these two issues, this paper introduces a new approach, called progressive band dimensionality process (PBDP) which performs progressive band dimensionality expansion and reduction via band prioritization (BP) which prioritizes the hyperspectral bands according to their priority scores calculated by a specific BP criterion. Two dual processes, referred to as forward PBDP (FPBDP) which performs band expansion in a forward manner and backward PBDP (BPBDP) which performs band dimensionality reduction in a backward manner. By virtue of its progressive nature the PBDP can be implemented by high computing performance while avoiding excessive computing time required by finding an optimal subset from all possible band subset combinations out of full bands. As a consequence, PBDP provides band selection with an advantage of not being trapped in high computational complexity resulting from solving combinatorial mathematics problems. A key to success in PBDP is how to design BP criteria to meet various applications. To address this need, four categories of BP are derived from different designing rationales, second order statistics, higher-order statistics, classification, and band correlation/dependence.