The interpretation of detailed spectroscopic observations of different stars reveals inconsistencies, due likely to inadequacies of the underlying hypothesis. The high accuracy of the parallaxes measured by the Hipparcos satellite established a firm reference frame that is used here to test theoretical classical model atmospheres for cool stars. Previously suspected errors in the ionization balance are clearly confirmed, pointing towards important departures from local thermodynamic equilibrium for low-gravity stars. We propose a method of semi-empirical modeling of stellar atmospheres, as an alternative to the use of flux-constant one-dimensional model atmospheres. The new method is carried out via an inversion procedure that uses normalized line profiles as input data. The procedure is applied to the Sun, showing its effectiveness through comparison with spatially resolved observations and absolute flux measurements. The application to other stars, in particular the metal-poor star Groombridge 1830, and the solar-like metallicity and active star Eps Eridani, yields semi-empirical model photospheres that succeed in reproducing all the considered spectral features. The very high-resolution spectra of Groombridge 1830 and the extremely metal deficient sub-giant HD140283 allow us to detect line asymmetries that are interpreted as the signature of convective patterns that, at least in HD140283, appear significantly enhanced due to the low atmospheric opacity. Finally, a survey for very metal poor stars in the Galaxy was conducted from the Isaac Newton Telescope at the Roque de los Muchachos Observatory in La Palma. In parallel, we develop a new method of classification of stellar spectra based on artificial neural networks, demonstrating its abilities and advantages against previously used schemes.