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The dynamics and stability of extragalactic jets may be strongly influencedby small (and probable) differences in pressure between the jet and the ambientand within the jet itself. The former give rise to expansion and recollimationof the jet. This occurs in the form of conical shocks, or Mach disks, if thepressure difference is large enough. Pressure asymmetries within the jet maytrigger the development of helical patterns via coupling to kink current-driveninstability, or to helical Kelvin-Helmholtz instability, depending on thephysical conditions in the jet. I summarize here the evidence collected duringthe last years on the presence of recollimation shocks and waves in jets. Inthe jet of CTA 102 evidence has been found for (traveling)shock-(standing)shockinteraction in the core-region (0.1 mas from the core), using information fromthe light-curve of the source combined with VLBI data. The conclusions derivedhave been confirmed by numerical simulations combined with emissioncalculations that have allowed to study the spectral evolution of the perturbedjet. Helical structures can also be identified in radio-jets. The ridge-line ofemission of the jet of S5~0836+710 has been identified as a physical structurecorresponding to a wave developing in the jet flow. I review here the evidencethat has allowed to reach this conclusion, along with an associated caveat.Current data do not allow to distinguish between magnetic or hydrodynamicalinstabilities. I finally discuss the importance of these linear and non-linearwaves for jet evolution.

Jet dynamics. Recollimation shocks and helical patterns