Measurements are reported for the temperature variation of ionic conductivity in single crystals of hexagonal silver iodide. Both nominally pure and Cu 2+ doped crystals were studied and analysis of the measurements for conduction both parallel and normal to the c-axis leads to a formation energy for Frenkel defects of 0-60 eV, activation energies for diffusion of Ag + interstitials parallel and normal to the c-axis of 0.61 and 0.29 eV respectively and corresponding activation energies for Ag + vacancies of 0-50 and 0.39 eV. Similar measurements performed on thin films of AgI grown expitaxially on mica show varying behaviour but the activation energy for conduction is about 0.4 eV, which agrees with the value expected from the single-crystal results if the conductivity is vacancy controlled. Dielectric measurements in the frequency range 10-10~Hz at temperatures between 193 and 340~ show anomalous dispersion peaks at about 104 Hz for temperatures above 300~ which are tentatively interpreted in terms of trapped Frenkel defects and interfacial polarization. At temperatures below about 290"K a series of sharp resonant absorptions is observed whose origin is uncertain. The static dielectric constant approaches the value 6.8 +-0.2 at temperatures below-40~ * Based on a thesis submitted by G. Cochrane for the Ph.D. degree of the University of New England.