Radiation at terahertz frequencies (wavelengths between 0.03 and 0.3 mm) can be used successfully to analyze the structural dynamics of water and biomolecules. But applying the technique to aqueous solutions and tissues remains challenging, since terahertz (THz) radiation is strongly absorbed by water. While this absorption enables certain analyses, such as the structure of water and its interactions with biological solutes, it limits the thickness of samples that can be analyzed, and it drowns out weaker signals from biomolecules of interest. Strong absorption of THz radiation in water has presented a bottleneck preventing THz radiation from revealing biophysical and biochemical processes deep within tissues.