Atmospheric particulate matter (PM) is a complex mixture of many different substances and requires a suite of instruments for chemical characterization. Fourier transform infrared (FT-IR) spectroscopy is a technique that can provide quantification of multiple species provided that accurate calibration models can be constructed to interpret the acquired spectra. In this capacity, FT-IR spectroscopy has enjoyed a long history in monitoring gas-phase constituents in the atmosphere and in stack emissions. However, application to PM poses a different set of challenges as the condensed-phase spectrum has broad, overlapping absorption peaks and contributions of scattering to the mid-infrared spectrum. Past approaches have used laboratory standards to build calibration models for prediction of inorganic substances or organic functional groups and predict their concentration in atmospheric PM mixtures by extrapolation. In this work, we review recent studies pursuing an alternate strategy, which is to build statistical calibration models for mid-IR spectra of PM using collocated ambient measurements. Focusing on calibrations with organic carbon (OC) and elemental carbon (EC) reported from thermal-optical reflectance (TOR), this synthesis serves to consolidate our knowledge for extending FT-IR spectroscopy to provide TOR-equivalent OC and EC measurements to new PM samples when TOR measurements are not available. We summarize methods for model specification, calibration sample selection, and model evaluation for these substances at several sites in two US national monitoring networks: seven sites in the Interagency Monitoring of Protected Visual Environments (IMPROVE) network for the year 2011 and 10 sites in the Chemical Speciation Network (CSN) for the year 2013. We then describe application of the model in an operational context for the IMPROVE network for samples collected in 2013 at six of the same sites as in 2011 and 11 additional sites. In addition to extending the evaluation to samples from a different year and different sites, we describe strategies for error anticipation due to precision and biases from the calibration model to assess model applicability for new spectra a priori. We conclude with a discussion regarding past work and future strategies for recalibration. In addition to targeting numerical accuracy, we encourage model interpretation to facilitate understanding of the underlying structural composition related to operationally defined quantities of TOR OC and EC from the vibrational modes in mid-IR deemed most informative for calibration. The paper is structured such that the life cycle of a statistical calibration model for FT-IR spectroscopy can be envisioned for any substance with IR-active vibrational modes, and more generally for instruments requiring ambient calibrations.