Aphids are serious pests of many agricultural crops. Therefore, a good understanding of their population dynamics is vitally important for crop protection. There have been several attempts made to forecast the abundance of aphids and develop expert systems to help farmers optimize prophylactic measures and minimize their costs. The advisory systems, however, did not receive general acceptance and disappointingly few forecasting systems are in use. The failure of models to predict aphid population dynamics for practical purposes is due to the extremely wild oscillations in aphid numbers caused by intrinsic (size, fecundity, mortality, migration rate) and external factors (weather, especially temperature). As a consequence, the predictions are unlikely to be robust enough for reliable forecasting, mainly because they depend on the course of weather during the season, which cannot be predicted. Here we present a critical review of existing models of aphid population dynamics, examine biological assumptions that are incorporated in the models and present one of the latest models of aphid metapopulation dynamics. We conclude that natural enemies are unlikely to affect aphid population dynamics late in the season, but may have an effect very early in the season, when aphid colonies are still small and predators might be able to reduce the numbers of these colonies. Empirical verification of this is still very weak, however, and further experiments on this aspect of predator prey dynamics should be undertaken.