Plasmas are ubiquitous in the Universe but rare on Earth where they are generated in the laboratory mainly to reproduce fusion reactions as on stars. Space Weather, particle beam acceleration, quasi-periodic current redistributions in a tokamak, solar flares, inertial confinement by super-intense laser pulses, or disk accretion on compact objects from the scale of stars to that of galaxies are only a few examples of the many spectacular manifestations of a plasma system. Understanding the nonlinear collective processes of plasmas spontaneously developing a multi-scale dynamics represents today one of the main challenges in physics, a frontier problem, because the weakness of the dissipation processes makes the plasmas remain in a state far from thermodynamic equilibrium as they evolve in time. In this seminar, after introducing the definition of a plasma system and its range of applications, I will discuss an example of a fundamental plasma process, namely the development of the Kelvin-Helmholtz instability, the generation of rolled-up vortices and their further transition to fully developed turbulence. Numerical simulations of this process with real parameters taken from the Earth Magnetosphere system will be compared to experimental data obtained from satellite space missions. The results presented here have been supported by a recent FP7 three years EU project. It is remarkable that similar processes, arising from the development of a K-H instability, also occur in non-neutral plasmas produced in the laboratory, as e.g. in the ELTRAP device, operating in the Physics Department of Milan University.