Spectroscopic techniques allow for studies of materials and organisms on the atomic and molecular level. Examples of such techniques are nuclear magnetic resonance (NMR) spectroscopy—one of the principal techniques to obtain physical, chemical, electronic and structural information about molecules—and magnetic resonance imaging (MRI)—an important medical imaging technique for, e.g., visualization of the internal structure of the human body. The less well-known spectroscopic technique of nuclear quadrupole resonance (NQR) is related to NMR and MRI but with the difference that no external magnetic field is needed. NQR has found applications in, e.g., detection of explosives and narcotics. The first part of this thesis is focused on detection and identification of solid and liquid explosives using both NQR and NMR data. Methods allowing for uncertainties in the assumed signal amplitudes are proposed, as well as methods for estimation of model parameters that allow for non-uniform sampling of the data. The second part treats two medical applications. Firstly, new, fast methods for parameter estimation in MRI data are presented. MRI can be used for, e.g., the diagnosis of anomalies in the skin or in the brain. The presented methods allow for a significant decrease in computational complexity without loss in performance. Secondly, the estimation of blood flow velo-city using medical ultrasound scanners is addressed. Information about anomalies in the blood flow dynamics is an important tool for the diagnosis of, for example, stenosis and atherosclerosis. The presented methods make no assumption on the sampling schemes, allowing for duplex mode transmissions where B-mode images are interleaved with the Doppler emissions.