  This document summarises the current theoretical and experimental status of
the di-Higgs boson production searches, and of the direct and indirect
constraints on the Higgs boson self-coupling, with the wish to serve as a
useful guide for the next years. The document discusses the theoretical status,
including state-of-the-art predictions for di-Higgs cross sections,
developments on the effective field theory approach, and studies on specific
new physics scenarios that can show up in the di-Higgs final state. The status
of di-Higgs searches and the direct and indirect constraints on the Higgs
self-coupling at the LHC are presented, with an overview of the relevant
experimental techniques, and covering all the variety of relevant signatures.
Finally, the capabilities of future colliders in determining the Higgs
self-coupling are addressed, comparing the projected precision that can be
obtained in such facilities. The work has started as the proceedings of the
Di-Higgs workshop at Colliders, held at Fermilab from the 4th to the 9th of
September 2018, but it went beyond the topics discussed at that workshop and
included further developments.
