The most direct, dynamical evidence for the presence of accretion disks in the central engines of active galaxies comes from observations of very broad, skewed and/or double-peaked emission lines. Examples include the Fe K lines observed in the X-ray spectra of Seyfert galaxies and the Balmer lines observed in the spectra of broad-line radio galaxies. Although the origin of double-peaked Balmer lines was the subject of debate in the past, the observational data available today make a strong case that they do indeed originate in an accretion disk. As such they can play two very important roles (a) they can guide us towards a general understanding of the dynamics of the broad emission-line gas in all active galaxies, and (b) they serve as diagnostics of dynamical and thermal phenomena in the accretion disk. Variability of the line profiles is the means by which we extract information on dynamical and thermal phenomena in the disk. The dynamical time in the line-emitting part of the disk is expected to be about six months, which is much longer than the light crossing time. Thus the slow variations of the line profiles over time scales of a few years can be used to test models for the dynamical behavior of the disk. These models include spiral waves, elliptical disks, and interactions of the disk with stars or gas clouds in its vicinity.