A search for Higgs boson pair production in the bbbb final state is carried out with up to 36.1 fb(-1) of LHC proton-proton collision data collected at s=13 TeV with the ATLAS detector in 2015 and 2016. Three benchmark signals are studied: a spin-2 graviton decaying into a Higgs boson pair, a scalar resonance decaying into a Higgs boson pair, and Standard Model non-resonant Higgs boson pair production. Two analyses are carried out, each implementing a particular technique for the event reconstruction that targets Higgs bosons reconstructed as pairs of jets or single boosted jets. The resonance mass range covered is 260-3000 GeV. The analyses are statistically combined and upper limits on the production cross section of Higgs boson pairs tim...