  Blazars are thought to emit highly-collimated outflows, so-called jets. By
their close alignment to our line of sight, relativistic beaming effects enable
us to observe these jets over the whole electromagnetic spectrum up to TeV
energies, making them ideal laboratories for studying jet physics. In the last
years multiwavelength observations of blazars provided us with detailed data
sets which helped to characterize the two main components of the
non-relativistic emission, peaking in the optical to X-ray and GeV/TeV energy
region, respectively. In leptonic acceleration models, they are explained by
synchrotron radiation of electrons and inverse-Compton emission from the same
electron population and thus, correlations of both emission regimes are
expected. We review recent observational results on the presence and absence of
such correlations in blazars, and discuss constraints on emission models by
quantitative correlation analyses.
