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Nuclear quadrupole resonance (NQR) is a solid-state radio frequency spectroscopic technique that can be used to detect the presence of quadrupolar nuclei, that are prevalent in many narcotics, drugs, and explosive materials. Similar to other modern spectroscopic techniques, such as nuclear magnetic resonance, and Raman spectroscopy, NQR also relies heavily on statistical signal processing systems for decision making and information extraction. This chapter provides an overview of the current state-of-the-art algorithms for detection, estimation, and classification of NQR signals. More specifically, the problem of NQR-based detection of illicit materials is considered in detail. Several single-and multi-sensor algorithms are reviewed that possess many features of practical importance, including (a) robustness to uncertainties in the assumed spectral amplitudes, (b) exploitation of the polymorphous nature of relevant compounds to improve detection, (c) ability to quantify mixtures, and (d) efficient estimation and cancellation of background noise and radio frequency interference.The authors are at