M dwarfs constitute around 70% of all stars in the local Galaxy. Their multitude together with their long main-sequence lifetimes make them important for studies of global properties of the Galaxy such as the initial mass function or the structure and kinematics of stellar populations. In addition, the exoplanet community is showing an increasing interest for those small, cold stars. However, very few M dwarfs are well characterized, and in the case of exoplanetary systems the stellar parameters have a direct influence on the derived planet properties. Stellar parameters of M dwarfs are difficult to determine because of their low surface temperatures that result in an optical spectrum dominated by molecular lines. Most previous works have therefore relied on empirical calibrations. High-resolution spectrographs operating in the infrared, a wavelength region less affected by molecular lines, have recently opened up a new window for the investigation of M dwarfs. In the two first papers of this thesis we have shown that we can determine the metallicity, and in some cases the effective temperature, using synthetic spectral fitting with improved accuracy. This method is time consuming and therefore not practical or even feasible for studies of large samples of M dwarfs. When comparing our results from the high-resolution studies with available photometric calibrations we find systematic differences. In the third paper we therefore used our sample to determine a new photometric metallicity calibration. Compared to previous calibrations our new photometric calibration shows improved statistical characteristics, and our calibration gives similar results as spectroscopic calibrations. In a comparison with theoretical calculations we find a good agreement of the shapes and slopes of iso-metallicity lines with our empirical relation. Applying the photometric calibration to a sample of M dwarfs with confirmed exoplanets we find a possible giant planet-metallicity correlation for M dwarfs.