This review highlights the opportunities of catalytic hydrolysis of NaBH₄ with the use of inexpensive and active Co-B catalysts among the other systems of hydrogen storage and generation based on water reactive materials. This process is important for the creation of H₂ generators required for the operation of portable compact power devices based on low-temperature proton exchange membrane fuel cells (LT PEM FC). Special attention is paid to the influence of the reaction medium on the formation of active state of Co-B catalysts and the problem of their deactivation in NaBH₄ solution stabilized by alkali. The novelty of this review consists in the discussion of basic designs of hydrogen generators based on NaBH₄ hydrolysis using cobalt catalysts and the challenges of their integration with LT PEM FC. The potential of using batch reactors in which there is no need to use aggressive alkaline NaBH₄ solutions is discussed. Solid-phase compositions or pellets based on NaBH₄ and cobalt-containing catalytic additives are proposed, the hydrogen generation from which starts immediately after the addition of water. The review made it possible to formulate the most acute problems, which require new sci-tech solutions.