A large collective effort to study the variability of active galactic
nuclei (AGN) over the past decade has led to a number of fundamental r
esults on radio-quiet AGN and blazars. In radio-quiet AGN, the ultravi
olet (UV) bump in low-luminosity objects is thermal emission from a de
nse medium, very probably an accretion disk, irradiated by the variabl
e X-ray source. The validity of this model for high-luminosity radio-q
uiet AGN is unclear because the relevant UV and X-ray observations are
lacking. The broad-line gas kinematics appears to be dominated by vir
ialized motions in the gravity field of a black hole, whose mass can b
e derived from the observed motions. The ''accretion disk plus wind''
model explains most of the variability (and other) data and appears to
be the most appropriate model at present. Future investigations are o
utlined. In blazars, rapid variability at the highest energies (gamma-
rays) implies that the whole continuum is relativistically boosted alo
ng the line of sight. The general correlation found between variations
in TeV gamma rays and in X rays for Mrk 421, and between variations i
n GeV gamma rays and in the IR-optical-UV bands for 3C 279, two protot
ype objects, supports models in which the same population of relativis
tic electrons radiates the low-frequency continuum via synchrotron and
the high frequency continuum via inverse Compton scattering of soft p
hotons. Identifying the dominant source of soft photons, which is at p
resent unclear, will strongly constrain the jet physics.