Among the hyperpolarization (HP) techniques, parahydrogen-based methods are the simplest and technically least demanding. Because such techniques (PHIP, SABRE) rely heavily on catalysis, some of the unsolved problems in both fields are rather similar. One major trend in modern catalysis is a broad search for approaches to combine advantages of homogeneous and heterogeneous catalysts, namely the well-defined structure of the active catalytic center of homogeneous catalysts for high reaction selectivity, and the ease of solid heterogeneous catalyst removal after the reaction. Similarly, it would be highly advantageous to combine the ability of a soluble transition metal complex to add H2 to a substrate in a pairwise manner, and the feasibility of rapid filtration of the reaction mixture to yield a metal-free HP fluid for biomedical use. Indeed, HP effects have been demonstrated lately with the use of several concepts of modern catalysis, including immobilization of transition metal complexes on porous solids, the use of single-site and single-metal-atom heterogeneous catalysts, and active site isolation in metal alloys and bimetallic structures. Heterogeneous catalysis is also suitable for production of HP propane as a promising agent for gas-phase imaging. Another recent breakthrough in modern catalysis is the demonstration that certain metal-free systems are able to activate small molecules such as H2. PHIP effects with the use of amine-borane frustrated Lewis pairs and other metal-free systems demonstrated recently may provide an alternative way to produce biocompatible HP solutions. Thus, the implementation of the achievements of modern catalysis in HP research can lead to a substantial progress in parahydrogen-based NMR signal enhancement, as will be illustrated with several recent examples. Furthermore, the HP techniques can be highly useful in addressing many challenges of modern catalysis research, to be exemplified with the mechanistic insight into the heterogeneous hydrogenation of cyclopropane and MRI of model hydrogenation reactors.