Comprehensive understanding of planets is predicated on detailed descriptions of their parent stars. M dwarfs are prolific hosts of planetary systems and form an important sample for the PLATO mission. The prospect for characterizing M dwarfs to a level comparable with Sun-like stars is bright, thanks to recent improvements in atmosphere models and the growing availability of high-resolution spectroscopic data. The CARMENES survey has produced high-quality, R~90,000, multi-epoch spectra in the optical and NIR for hundreds of nearby early- to late-M dwarfs. These spectra have been accurately telluric-corrected and co-added to very high signal-to-noise, making them suitable for identifying and modeling fine features intrinsic to the star. The wavelength coverage (520 — 1710 nm) of the CARMENES spectrograph is one of the widest in the industry and contains a large variety of lines and features. Their resolved profiles are sensitive to temperature, metallicity, elemental abundances, and exhibit useful quantum effects. We give examples of recent applications using CARMENES spectra to measure fundamental stellar parameters and chemical compositions of M dwarf photospheres. We summarize how lessons from CARMENES spectroscopy of cool dwarfs could inform target selection and characterization efforts from ground-based facilities for PLATO. (Contributed talk to PLATO mission conference, Oct 2021)