Models of variability in blazar jets

We present the expected variability features in the context of the Synchro- Self-Compton (SSC) model of emission from Active Galactic Nuclei (AGNs) and show that the homogeneous SSC model describes well the observed multi- wavelength spectrum and variability of objects such as Mkn 421 and Mkn 501; however in order to explain the very fast flaring timescales occasionally observed from these objects one should use a laminar, rather than spherical, source geometry. This picture leads naturally to a shock-in- jet model which we approach as a site of diffusive particle acceleration. We show that this acceleration scheme can explain certain characteristic features of AGN X-ray spectra and provides us with further observational tests.