One step closer to probe the nature of the Higgs boson

A decade after its discovery the Higgs boson remains central to many open questions in particle physics. For example, the shape of the Higgs field potential is key to understand the nature of the electroweak symmetry breaking. Experimentally, the Higgs boson self-interaction, that is, the splitting of one Higgs boson into two or even three Higgs bosons provides the most direct way to constrain this shape. In this talk, we review the latest searches for this signature at the Large Hadron Collider (LHC) and interpret the results in terms of contraints of the Higgs boson self-interaction. We also review experimental progress to pin down this very rare signature and review prospects for the future large dataset to be collected at the next phase of the LHC.