The interpretation of detailed spectroscopic observations of late‐type stars reveals inconsistencies that are likely due 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 these stars. Stellar gravities derived making use of the Hipparcos parallaxes and stellar evolution models are compared with spectroscopic (iron ionization equilibrium) gravities. Previously suspected errors in the ionization balance are clearly confirmed, which points toward important departures from local thermodynamic equilibrium for low‐gravity stars as a possible explanation. We propose a method of semiempirical 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, named MISS, that uses normalized line profiles as input data. The algorithm assumes LTE, a steady state, plane‐parallel, one‐dimensional atmosphere, solid body rotation, hydrostatic equilibrium, and negligible magnetic field. The procedure is applied to the Sun, showing its effectiveness through comparison of its predictions 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 ϵ Eridani, yields semiempirical model photospheres that succeed in reproducing all the considered spectral features (not included in the inversion procedure). Very high resolution spectra of Groombridge 1830 and the extremely metal deficient subgiant HD 140283, acquired at the McDonald Observatory 2.7 m telescope, allow us to detect line asymmetries that are interpreted as the signature of convective patterns that, at least in HD 140283, appear significantly enhanced owing to the low atmospheric opacity. Strong differences are observed between the line bisector of photospheric atomic lines and the Mg i b1 and b2 lines, in the spectrum of HD 140283. The lower part of the line bisector of the strong magnesium features, whose cores are formed higher in the atmosphere than the photospheric lines, appear remarkably bent to the red. This is compatible with the high‐velocity redshifts observed in the spectral lines formed in the chromosphere, transition region, and corona of late‐type stars. It is shown how not only the line asymmetries but also the relative line shifts can be used in the Sun and other stars to extract useful information about velocity fields and atmospheric inhomogeneities. We have traced the strengthening of the convective blueshifts toward deeper layers in the solar photosphere. The cores of the strong solar lines appear to be almost free of net convective shifts, a property that might be used to separate the stellar radial velocity and the gravitational redshift from the photospheric motions in solar‐like stars. Finally, a search 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 developed a new method of classification of stellar spectra based on artificial neural networks, demonstrating its abilities and advantages against previously used schemes. The acquired medium‐resolution spectra are shown to be useful for estimating the stellar metallicity and the B−V color. The survey has provided spectra for more than 1000 objects of which 709 have been identified as late‐type stars. Almost every star in the sample is metal deficient compared to the Sun: 26 are of , 87 of , and 210 of .