A theoretical review of triple Higgs coupling studies at the LHC in the Standard Model

After the discovery of a Higgs boson at the LHC, the next important step is to measure its couplings to fermions and bosons to unravel its true nature. In order to ultimately test the shape of the scalar potential that triggers the electroweak symmetry breaking, it is crucial to measure the triple Higgs coupling at the LHC. We then review the theoretical predictions of the main Standard Model Higgs pair production mechanisms that are needed for such a measurement and present the latest developments in the phenomenological analyses in view of a high luminosity LHC.