The Future Circular Collider study is exploring possible designs of circular colliders for the post-LHC era, as recommended by the European Strategy Group for High Energy Physics. One such option is FCC-hh, a proton-proton collider with a centre-of-mass energy of 100 TeV. The experimental insertion regions are key areas defining the performance of the collider. This paper presents the first insertion region designs with a complete assessment of the main challenges, as collision debris with two orders of magnitude larger power than current colliders, beam-beam interactions in long insertions, dynamic aperture for optics with peak $beta$ functions one order of magnitude above current colliders, photon background from synchrotron radiation and cross talk between the insertion regions. An alternative design avoiding the use of crab cavities with a small impact on performance is also presented.