Projection matrix models are widely used in population biology to project the present state of a population into the future, either as an attempt to forecast population dynamics, or as a way to evaluate life history hypotheses. These models are flexible and mathematically relatively easy. They have been applied to a broad range of plants and animals. The asymptotic properties of projection matrices have clearly defined biological interpretations, and the analysis of the effects of perturbations on these asymptotic properties offers new possibilities for comparative life history analysis. The connection between projection matrix models and the secondary theorem of natural selection opens life cycle phenomena to evolutionary interpretation.