Data on the complex dielectric permittivity of ice around megahertz frequencies are reviewed with additions of a few new data sets. Then propagation of electromagnetic waves in the ice sheets is examined. Our purpose is to establish an updated data set to link ice sheet structure (or ice core signals) to radar sounding data. The complex permittivity of ice in the ice sheets is a function of several controlling factors as follows: (1) crystal orientation fabrics, (2) density, (3) impurity concentration (mainly acidity), and (4) temperature. In contrast, both (5) hydrostatic pressure and (6) air-bubble shape have relatively minor effects. The effect of (7) plastic deformation can be significant and needs to be investigated further. The phase velocity of electromagnetic waves in ice is 168.0~169.5 (m1/-Ls). Present data scatter is about I %, probably due to the small dispersion between LF and microwaves, or due to experimental errors in the present data sets. Attenuation is controlled mainly by conductivity arising from the presence of acidity. Because of this dominant acidity effect, the attenuation coefficient is virtually independent of frequency up to several hundred megahertz. As for internal reflections, the three major causes that have been proposed earlier are now conclusive: changes in (1), (2) and (3). We find the nature of complex reflection coefficients to be as follows. For reflections based on (1) and (2) the amplitude of the complex coefficient is independent of both ice temperature and frequency; the phase delay is virtually zero. In contrast, for reflections based on (3), the amplitude is inversely proportional to frequency, and it is strongly dependent also on temperature. Because the imaginary components are dominant, the phase delay varies between 0.98 and 0.89 (x rrJ2 radian). These results suggest that each of the physical factors can be solved quantitatively by analysis of remote sensing data, using frequency and temperature as key parameters.