A comprehensive theoretical model of laser induced plasma has been developed, interfaced, and applied to spectrochemical analysis and plasma diagnostics. The model incorporates many physical chemical processes which allow for the precise description and better understanding of analytical plasmas, specifically, plasmas used in Laser Induced Breakdown Spectroscopy (LIBS) and Inductively Coupled Plasma (ICP) spectroscopy. The modeled features include viscous flow with shock formation, diffusion, convection, chemical kinetics, radiation loss, and radiation transfer. The model is carefully verified for its capability to reproduce a full variety of spectra observed in LIBS experiments. On a practical side, the feasibility of calibration-free analysis was proved via synthesizing theoretical spectra using the model and matching them to experimental spectra. This approach was applied to analysis of aluminum alloys and geological samples. Our version of calibration-free LIBS provides semi-quantitative results that are 50-100% accurate for trace elements and 10-50% accurate for major constituents. Despite the modest accuracy, this type of analysis is in great demand for field applications and harsh environments. A series of plasma diagnostics was carried out aimed at better understanding of matrix effect that hampers accuracy of LIBS. Here, spatially-temporal mapping of plasma species (atoms, ions, and molecules) was done using the traditional Abel tomography and more general Radon tomography, which was first applied to LIBS. Also, limits of applicability of different diagnostic methods, such as the Boltzmann plot and Abel inversion methods were set by numerical experiments with the plasma model. The latter provides practical recommendations to experimentalists of how to correctly set experiment and to process and interpret spectroscopic data.