During the last decade, our groups have performed systematic experimental studies on the characterization of plasma plumes generated by laser ablation in various temporal regimes (ns, ps, fs) on materials ranging from simple metals (Al, Cu, Mn, Ni, In, W, …) to more complex compounds (ceramics, chalcogenide glasses, ferrites). Optical (fast imaging and space-and time-resolved emission spectroscopy) and electrical (mainly Langmuir probe) methods have been applied to experimentally investigate the dynamics of the plasma plume and its constituents. Influence of the target physical (thermodynamic and electrical) parameters on the plasma dynamics has been studied. A mathematical correlation between the local and global plasma parameters and the physical properties of the target was proposed for the first time. Peculiar behaviors like plume splitting or plasma oscillations have been evidenced for high laser fluence ablation in vacuum. Along with results from the literature, our findings provide convincing arguments for the existence of multiple double-layers in the laser ablation plasma plume, in a scenario including two-temperature electrons. New fractal-based theoretical approaches have been developed to qualitatively and quantitatively account for the observed phenomena. The space and time evolution of expansion velocity, particle number, current density and plasma temperature were theoretically investigated.