The discovery of the Higgs boson in 2012 provided the first direct probe of the Higgs potential in experimental physics, opening the doors to an unprecedented era of precision Higgs measurements at the LHC (and hopefully beyond!) A natural extension is to probe the global shape of the Higgs potential, which will provide direct insights into the stability of our universe and its early cosmology. At the LHC we are working to achieve just this through measuring the Higgs self-coupling in di-Higgs production. This seminar will present the latest results from the ATLAS experiment on searches for di-Higgs production, the latest constraints on the Higgs self-coupling, and smoking gun signatures for di-Higgs production from BSM matter. Prospects for future studies at the HL-LHC and potential cosmological consequences of a BSM Higgs self-coupling will also be presented.