Jets appear to be ubiquitous in accreting systems, but the origin of the observed accretion disc-jet coupling remain largely unknown. In this project we propose to use a twofold, observational and theoretical, approach to study and understand the internal physics, structure and variability of jets in accreting black holes, neutron stars and white dwarfs, as well as their coupling with the accretion disc. Observational approach: we will take advantage of newly available technologies on large telescopes, and we will apply advanced timing-analysis techniques to a wealth of data over the whole electromagnetic spectrum. The study of correlated fast multi-wavelength variability has a great and largely unexplored potential to help solving many open issues. Coordinated X-ray, infrared, optical and radio observations at high time resolution will unveil the origin of multiwavelength emission in accreting compact objects. To observe and identify the timescales of the variability at different wavelength is our best chance to study the physical processes, the accretion geometry that yield to the ejection of relativistic matter, as well as the geometry and variability of the jet itself. To compare the properties of correlated variability in accreting black holes, neutron stars and white dwarfs will allow us to investigate the role of the black hole spin in producing and powering the jet, and to unify for the first time the science of accretion and jet formation. Theoretical approach: we will support these observations with a deep theoretical effort, both numerical and analytical. The emission from jet internal shocks in the mildly-relativistic case will be modeled analytically, and the jet variability as a function of a variable accretion rate will be simulated. A self-consistent model for the jet structure and variability in X-ray binaries will be developed, and tested against the data.