We sketch the evolution of station trajectory models used in crustal motion geodesy over the last several decades, and describe some recent generalizations of these models that allow geodesists and geophysicists to parameterize accelerating patterns of displacement in general, and postseismic transient deformation in particular. Modern trajectory models are composed of three sub-models that represent secular trends, annual oscillations, and instantaneous jumps in coordinate time series. Traditionally the trend model invoked constant station velocity.