Our new approach to mobility measurement involves separating out the valuation of positions in terms of individual status (using income, social rank, or other criteria) from the issue of movement between positions. The quantification of movement is addressed using a general concept of distance between positions and a parsimonious set of axioms that characterize the distance concept and yield a class of aggregative indices. This class of indices induces a superclass of mobility measures over the different status concepts consistent with the same underlying data. We investigate the statistical inference of mobility indices using two well-known status concepts, related to income mobility and rank mobility. We also show how our superclass provides a more consistent and intuitive approach to mobility, in contrast to other measures in the literature, and illustrate its performance using recent data from China.