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The paper describes past and present efforts in modeling of laser-induced plasma and overviews plasma diagnostics carried out by pump-probe techniques. Besides general information on existing plasma models, the emphasis is given to models relevant to spectrochemical analysis, i.e. models of radiating plasma. Special attention is paid to collisional-radiative (CR) and collisional-dominated (CD) plasma models where radiative processes play an important role. Also, calibration-free (CF) models are considered which may endow with the possibility for standardless spectroscopic analysis. In the diagnostic part, only methods based on the use of additional diagnostic tools (auxiliary lasers, optics, and probes) are described omitting those based on plasma own radiation. A short review is provided on image-based diagnostics (shadowgraphy, schlieren, and interferometry), absorption and fluorescence, Langmuir probe, and less frequently used cavity ringdown and Thomson scattering methods.