In the Standard Model, the ground state of the Higgs field is found at one of the non-zero minima of the Higgs potential. In turn, this spontaneous electroweak symmetry breaking provides a mechanism to generate the mass of nearly all fundamental particles. The Standard Model makes a definite prediction for the Higgs boson self-interaction and thereby the shape of the Higgs potential. Experimentally, both can be probed through the production of Higgs boson pairs (HH) at the LHC. In this talk, the latest HH searches by the ATLAS and CMS collaborations are reported, with emphasis on the results obtained with the full LHC Run 2 dataset at 13 TeV, and their statistical combinations. Prospect for observing HH and measuring the Higgs boson self-interaction at the High-Luminosity LHC are also discussed.