When measured with sufficient spectral range, resolution, and signal-to-noise ratio, nearly every mineral has a unique infrared spectral signature. However, determining which minerals are present on Mars using infrared spectroscopy has proven to be very difficult. The goal of this work is to examine complicating factors inherent to spacecraft-based infrared spectral measurements of Mars, and to determine methods to extract mineralogical information from spectra that cover the wavelength range 0.77 to 50 mum. On Earth, infrared spectra of an unknown mineral or gas can be measured under controlled conditions. However, a spacecraft spectrometer measures Mars through both atmospheric gases and aerosols, and at varying viewing geometries. Spectra of the surface of Mars have very subtle variations, so examining them requires well-calibrated spectra of excellent quality, and extended spectral range. These combined effects greatly complicate interpretations. The work presented here details a straightforward method to remove effects of varying viewing geometry on near-infrared spectra of Mars, using 1989 Phobos 2 ISM spectra. Next, it details the recovery and calibration of the 1969 Mariner Mars IRS data set, and presents IRS spectral evidence for goethite on Mars. Finally, a method is developed to utilize night spectra to examine the aerosol mineralogy, followed by a discussion of the importance of accounting for the aerosol re-emission when utilizing day measurements to examine surface mineralogy. This work utilizes spectra from all five infrared spectrometers flown to Mars. It addresses a range of issues, but the unifying theme is how to extract mineralogic information from the spectra. The results show that the most important spectral criteria for determining mineralogy from spacecraft infrared spectra are an extended spectral range, high spectral resolution, and high signal-to-noise ratio. Here, an extended spectral range is defined as coverage of at least two of the three infrared spectral regions: reflected (∼0.8--3 mum), overtone (∼3--7 mum), and fundamental (∼7--50 mum). Spectra with low spectral resolution, low spectral range, or low signal-to-noise ratio allow different spectral type units to be mapped, but such data sets do not provide enough information to determine uniquely the mineral phases present.