This thesis is concerned with layered reflections observed in the Antarctic and Greenland ice sheets during radio-echo sounding. It describes in detail layering seen with 60 and 300 MHz equipment _in the Antarctic ice sheet during three field seasons betwe~n 1974 and 1979, and discusses the effects of glaciological and equipment factors, particularly radio pulse length. The effects of changing pulse length and accumulation rate on layer echo separation are analysed, and the importance of closely spaced groups of reflectors assessed. Reflection coefficient vs depth profiles are presented for layering observed at nearly twenty sites in the Antarctic and Greenland, and are used to demonstrate the existence of two separate reflection mechanisms: changes in (a) ice density, and (b) loss tangent. Supporting density and conductivity data from ice cores are summarised. It is concluded that most layer echoes arise from layers of ice containing acidic impurities of volcanic origin~ Layer reflectivity variations_are observed over distances of tens of kilometres. Short-period fading is also observed, from which estimates of layer reflector roughness are made using the autocorrelation function and variance of the received power. The roughness estimates are shown to be consistent with a depositional origin for the surfaces. Relevant theory is summarised and a procedure developed for the remote estimation of elevated acidity levels in ice from radio-echo sounding. Such estimates are shown to compare well with direct ice core measurements. The method is used to present estimated elevated acidity profiles for the Antarctic (to ~100 kaBP) and Greenland (to ~30 kaBP), which are interpreted in terms of variations in the input of volcanogenic acid impurities to the ice sheets. The use of layering as isochronous horizons in ice flow studies is discussed in the light of new measurements, with particular emphasis on t he zone close to bedrock.