Research using shape data from geometric morphometric (GM) methods in ecology and evolutionary biology is typically comparative, analyzing shapes and shape change over different points along ecological or evolutionary gradients. Whereas standard multivariate statistics procedures are fine for "static" variation - testing for location differences of groups in multivariate data spaces - they are limited for "dynamic" variation - testing specific differences in the ways groups change locations associated with changes in state along ecological, developmental or evolutionary gradients. In this paper, we show that continuous phenotypic change can be described by trajectories in multivariate data spaces. We describe the geometric attributes of phenotypic change trajectories (size, direction, and shape), specifically for GM data. We illustrate, with examples, how differences in such attributes can function as test statistics for comparative analyses in order to understand the mechanisms that produce dynamic differences in shape change. We demonstrate that analysis of such attributes - called phenotypic trajectory analysis (PTA) - is a general analysis that can be applied to various types of research questions concerned with measuring dynamic variation. Finally, we posit some challenges for the future for this novel analytical method.