In this review, we have introduced four methods for activation of hydrogen molecules We started with the most conventional method, which is using metal and alloy to activate H2 molecules. We first introduced the Horiuti-Polanyi mechanism and non-Horiuti-Polanyi mechanism, providing a picture of the development of understanding. Secondly, we moved to transition-metal complex catalysis, another transition-metal-based approach, which is more controllable and can be used under milder conditions. However, there are some limitations that widely exist in metallic catalysis. For instance, the metal catalyst is difficult to be recycled, and it brings environmental problems. So, we also introduced two strategies that offer some potential to realize the metal-free dihydrogen activation. Divalent maingroup activation has a similar mechanism as oxidative addition of metal complexes, whereas FLPs catalysis has a significantly different mechanism. Asymmetric FLPs also provide a method of inducing chiral centres, which can be widely used in asymmetric synthesis. But the selectivity of FLPs catalysis still needs to be improved.