Nonlinear optical spectroscopy has emerged as a powerful tool for the investigation of crystalline solids. Compared to linear approaches, it offers additional experimental degrees of freedom which grant access to the sample's symmetry properties and can provide unique insight into its crystallographic and electronic structure. Moreover, owing to their higher-order field dependence, nonlinear techniques often feature improved contrast and sensitivity. These qualities are particularly useful in the infrared (IR) spectral region as it contains optical phonon resonances which carry symmetry information themselves and play a key role in determining a material's thermal, IR optical, and phase transition properties. Among nonlinear optical techniques, second-harmonic generation (SHG) takes on a prominent role as the simplest even-order process and, while widely employed in the visible, has so far not been fully exploited in the IR—mainly due to the scarcity of suitable laser sources. With access to an IR free-electron laser (FEL), however, it becomes feasible to employ IR SHG as a phonon spectroscopy. This work explores the potential of second-harmonic phonon spectroscopy as an alternative to more established even-order techniques. To this end, a comprehensive IR SHG study of the well-known model system α-quartz is performed, presenting the technique as a highly sensitive tool to study optical phonons in noncentrosymmetric polar crystals. Through these vibrational resonances, IR SHG can also aptly probe and characterize symmetry changes in a material which is demonstrated in a temperature-dependent study of quartz's α–β phase transition. The implementation of a cryogenic IR SHG setup extends the temperature range of second-harmonic phonon spectroscopy and enables phase transition studies at low temperatures where it also benefits from decreased phonon damping rates. Further, second-harmonic phonon spectroscopy was successfully employed in the characterization of the unique phonon modes emerging in atomic-scale superlattices which cause a distinct dielectric response, highly suitable for nanophotonic device applications. An attempt to exploit the technique's sensitivity to structural phase transitions in multiferroic thin films, revealed fundamental limitations of IR SHG posed by the relatively large IR FEL spot sizes and low sensitivity of available IR detectors. A proof-of-principle FEL-based IR-visible sum-frequency generation experiment shows how these limitations can be lifted while maintaining nonlinear optical and IR-resonant capabilities. Overall, this work comprehensively explores the potential of IR SHG as a phonon spectroscopy, showcasing its unique capabilities and identifying its limitations. Perspectives are presented on how to further develop FEL-based nonlinear optical approaches to which the present work constitutes important groundwork.