There is broad recognition that early life growth trajectories can contribute to the study of the onset and development of several health outcomes. We review the random-effects specifications of two models that have been purposely developed to describe anthropometric data and a shape invariant random-effects model recently proposed in the statistical literature. They are compared in terms of their ability to extract salient and biologically meaningful features of growth in infancy and also to represent the data validly. We discuss advantages and limitations in choosing and interpreting each of the models by using longitudinal weight data taken from 0 to 4 years from three contemporary birth cohorts.