The ratio of oxygen isotopes in glacial ice is often used as an indicator of climatic conditions during the period of time in which the ice was deposited. We have developed a model which predicts the isotopic composition of snow, given the composition of the source water and the meteorological path between the formation of an air-water parcel in the boundary layer and the final deposition of precipitation onto the ice sheets. After comparing the model results with isotope data from the present, we draw inferences about the past isotopic composition of continental ice sheets. Our results depend strongly on the details of the meteorological path. They are consistent with standard interpretations of isotope data, but in some cases they allow alternate interpretations.