Deterministic models developed to predict fatigue crack growth in metallic materials are considered with special emphasis on approaches suitable for variable amplitude load histories. Part I gives a concise review of available models and their assessment based on reported in the literature comparisons between predicted and observed results. It is concluded that the so-called strip yield model based on the plasticity induce crack closure mechanism is a most versatile predictive tool convenient to use in the case of mode I crack growth under arbitrary variable amplitude loading. Part II of the paper is focused on the strip yield model and its predictive capabilities. Implementations of this type prediction approach reported in the literature are reviewed. It is shown that decisions regarding the constraint factor conception, a choice of the crack driving force parameter, the crack growth rate description and various numerical details can have a profound effect on the model results and the prediction quality.