Modern ice sheets are currently responding to significant climatic forcings and undergoing ice-dynamics changes that are not yet well understood. Ice-penetrating radar surveys are often used to infer their basal condition (e.g., is the bed wet or dry?) and internal properties. However, such inferences typically require a model of the electromagnetic attenuation through the ice sheet. Here I first develop and test a radar-attenuation model that is based on a synthesis of existing laboratory measurements of the dielectric properties of ice. This synthesis shows that radar attenuation in polar ice has a strong non-linear temperature dependence and a weaker linear dependence on the concentrations of acid and sea-salt chloride. This model was tested at Siple Dome, West Antarctica, using ice-core-chemistry and borehole-temperature data, and the model agreed well with an existing radar-attenuation measurement. I then use this model to investigate the nature of radar detection of accreted ice over Lake Vostok, East Antarctica. My analysis of ice-core and radar data found that the observed reflection is likely due to a fabric contrast near the boundary between the dirty and clean accreted ices. This reflection mechanism is also consistent with the spatial pattern of detection of the reflection. In anticipation of the requirements of a thermomechanical ice-sheet model to predict the spatial variation of attenuation over Lake Vostok, I develop an accumulation-rate map for the Lake Vostok region using radar data, a steady-state flow-band model, and inverse methods. I found that accumulation rates there are not inversely correlated with surface elevation, that there is a broad maximum above the lake's northwestern corner, and a minimum above most of its eastern shoreline. Finally, I investigate the spatial variability of attenuation in an ice sheet, using the flowline that crosses through the Vostok ice core as an example. I use radar layers and ice-velocity and temperature outputs from an ice-sheet model to estimate the spatial variation of attenuation using a series of progressively more complex models. I found that an attenuation-rate model that uses non-uniform ice temperatures and radar layers to rescale impurity-conentration profiles can satisfactorily capture most of the spatial variability of attenuation.