Hyperpolarization of nuclear spins in molecules far beyond the thermal equilibrium levels achievable with modern high-field NMR spectrometers is very promising for boosting the sensitivity of NMR and MRI by four orders of magnitude, and even more in lower magnetic fields of bench-top and portable instruments. We describe the hyperpolarization approach based on the use of parahydrogen in hydrogenations of unsaturated compounds, and its emerging applications for advanced spectroscopic and imaging studies in catalysis and life sciences. Magnetic materials are efficient catalysts for the ortho-para conversion of H2 required to produce enriched parahydrogen at cryogenic temperatures. Furthermore, to produce reaction products with highly polarized nuclear spins, a catalyst able to efficiently perform pairwise H2 addition to an unsaturated substrate molecule is required. Observation of parahydrogen-induced polarization is feasible with the use of both heterogeneous and homogeneous catalysts, possibly including paramagnetic and superparamagnetic nanoparticles. This may open new ways of using catalytically active functionalized magnetic nanoparticles for the production of hyperpolarized substances followed by a facile catalyst separation. Removing the catalyst within seconds of completion of the hydrogenation process to produce catalyst-free solutions is one of the major current challenges in this field, especially for the in vivo use of hyperpolarized metabolites.