The environments underneath ice sheets are of high scientific interest. Wireless sensors offer the prospect of sustained, distributed remote sensing in the subglacial environment. Typically, wireless sensor networks use radio-frequency (RF) electromagnetic communications, but these are highly attenuated in wet environments. In such environments, acoustic communications may be more power-efficient. Here we review the literature on acoustic and RF attenuation through ice and other relevant media, and present the results of new experiments on acoustic attenuation in glacial ice. Link budgets for communications from a range of subglacial environments show that acoustic communications are a viable strategy for transmission through water and ice where RF is too highly attenuated to be detected. Acoustic communication at 30 kHz is predicted to be possible through 1 km of glacial ice, using a 1 W transmitter. Such a strategy may be appropriate for shallow ice-stream environments around the Antarctic and Greenland ice sheet margins.