AO 0235+164 is a very compact, flat-spectrum radio source. It is identified with a BL Lac object, and has optical absorption-line systems at z = 0.524 and z = 0.852. A complex set of HI absorption lines is seen at z = 0.524 (932 MHz), and several of these lines change significantly in depth over periods of less than a year. This is the only known case of variable extragalactic absorption lines. A faint nebulosity 2 arcsec south of AO 0235 + 164 has an emission-line redshift of z = 0.52 and may be an intervening galaxy. The radio spectrum of this source (between major outbursts) is remarkably flat, with the total flux density staying between about 1 and 3 Jy over a range of at least 1000 in frequency. Such a flat spectrum would lead one to expect a complex, wavelength-dependent structure consisting of several components with different self-absorption frequencies. However, the observed radio structure of 0235+164 is about as simple as one could imagine – it is a nearly unresolved point source in VLBI experiments from 900 MHz to 22 GHz. Recent VLBI experiments at 6 and 13 cm have shown evidence for some elongation of the source in a generally NE-SW direction, but only at low contour levels (< 15% of the peak). The major portion of the flux density appears to come from a core which is unresolved in VLBI experiments over a range of ~ 25 in frequency.