| Hedemarken Steinerskole | Hedemarken Steinerskole | Norway, Ottestad, Stange | 2002-05-12 | -- | 2002 | 1 | |
| Heistad ungdomsskole | Heistad ungdomsskole | Norway, Porsgrunn, Gamle Breviksveg 107 | 2005-10-04 | 2006-10-18 | 2005–2006 | 2 | |
| Heistad skole | Heistad skole | Norway, Porsgrunn, Lundedalen 35 | 2006-10-16 | -- | 2006 | 1 | |
| Heimtun | Heimtun | Norway, Rissa | 1956-06-21 | -- | 1956–1959 | 2 | |
| Havnescenen | Havnescenen | Norway, Risør, Risør | 2008-08-01 | -- | 2008 | 1 | |
| Haugeåsen Ungdomskole | Haugeåsen Ungdomskole | Norway, Rolvsøy, Fredrikstad | 2006-11-08 | -- | 2006 | 1 | |
| Halmstad Ungdomsskole | Halmstad Ungdomsskole | Norway, Rygge, Skoleveien 4 | 2005-10-26 | -- | 2005 | 1 | |
| Hjertnes Kulturhus | Hjertnes Kulturhus | Norway, Sandefjord, Sandefjordsveien 3 | 1978-01-11 | 2020-11-02 | 1978–2022 | 20 | |
| Hotell Høyer | Hotell Høyer | Norway, Skien, Kongens gate 6 | 2006-10-03 | -- | 2006 | 1 | |
| Hjelseth brygge, Telemarkskanalen | Hjelseth brygge, Telemarkskanalen | Norway, Skien, Skotfoss | 2006-05-23 | 2006-06-15 | 2006 | 1 | |
| Henrik Ibsen Museum | Henrik Ibsen Museum | Norway, Skien, Venstøp | 1992-06-11 | 2019-07-31 | 1992–2019 | 3 | |
| Henrik Ibsen's Museum Venstøp | Henrik Ibsen's Museum Venstøp | Norway, Skien, Venstøphøgda 74 | 2001-08-04 | 2010-10-28 | 2001–2010 | 3 | |
| Hassel fengsel | Hassel fengsel | Norway, Skotselv | 2012-12-04 | -- | 2012 | 2 | |
| Herredshuset | Herredshuset | Norway, Sortland | 1968-09-12 | -- | 1968 | 1 | |
| Harøy Samfunnshus | Harøy Samfunnshus | Norway, Steinshamn | 1973-10-07 | -- | 1973–1990 | 2 | |
| Hurtigrutens Hus | Hurtigrutens Hus | Norway, Stokmarknes, Markedsgata 1 | 2009-09-04 | 2020-10-13 | 2009–2022 | 6 | |
| Haugar Vestfold Kunstmuseum | Haugar Vestfold Kunstmuseum | Norway, Tonsberg, Gråbrødregaten 17 | 1993-06-25 | -- | 1993 | 1 | |
| Hålogaland Teater | Hålogaland Teater | Norway, Tromsø, Teaterplassen 1 | 1972-10-20 | 2019-10-12 | 1972–2019 | 15 | |
| Herredshuset | Herredshuset | Norway, Trysil | 1969-09-30 | -- | 1969–1973 | 2 | |
| Hovinsetra | Hovinsetra | Norway, Tyrifjord | 2010-08-07 | -- | 2010 | 1 | |
| Holla ungdomsskole | Holla ungdomsskole | Norway, Ulefoss, Nome | 2004-09-07 | 2004-09-09 | 2004 | 1 | |
| Helland skule | Helland skule | Norway, Vestnes, Vestnes | 2006-09-19 | -- | 2006 | 1 | |
| Herredshuset | Herredshuset | Norway, Voss | 1960-10-26 | 1963-03-30 | 1960–1963 | 3 | |
| Herredshuset | Herredshuset | Norway, Åsnes | 1959-01-20 | -- | 1959 | 1 | |
| Halhool Yard, Hebron | Halhool Yard, Hebron | Palestinian Territories, Hebron | 2008-10-16 | -- | 2008 | 1 | |
| Hajdpark, Teatr Wytwórni | Hajdpark, Teatr Wytwórni | Poland, Warsaw | 2006-08-23 | -- | 2006 | 1 | |
| Hațeg | Hațeg | Romania, Hațeg | 1911-09-11 | -- | 1911 | 1 | |
| Huedin | Huedin | Romania, Huedin | -- | -- | | | |
| Hunedoara | Hunedoara | Romania, Hunedoara | 1913-10-17 | -- | 1913 | 1 | |
| Huși | Huși | Romania, Huși | -- | -- | | | |
| His Majesty’s Theatre | His Majesty’s Theatre | Scotland, Aberdeen, Rosemount Viaduct | 1972-05-01 | 2017-11-25 | 1972–2017 | 4 | |
| Her Majesty's Theatre | Her Majesty's Theatre | Scotland, Dundee, Seagate | 1897-08-02 | -- | 1897 | 1 | |
| Hill Street Theatre | Hill Street Theatre | Scotland, Edinburgh, 19 Hill Street | 2006-08-04 | 2011-08-29 | 2006–2011 | 2 | |
| Hub, The | The Hub | Scotland, Edinburgh, Castlehill | 2008-08-25 | 2008-08-27 | 2008 | 1 | |
| Hexagon Studio Theatre | Hexagon Studio Theatre | South Africa, Pietermaritzburg, KwaZulu-Natal, UKZN, Golf Rd | 2006-10-25 | 2006-10-28 | 2006 | 1 | |
| HB Thom Theatre | HB Thom Theatre | South Africa, Stellenbosch, 15 Victoria St | 2012-09-18 | 2012-09-22 | 2012 | 2 | |
| Hambantota | Hambantota | Sri Lanka, Hambantota | 2006-10-18 | -- | 2006 | 1 | |
| Handelsinstitutets sal | Handelsinstitutets sal | Sweden, Göteborg | 1903-01-20 | -- | 1903 | 1 | |
| Hallstahammar | Hallstahammar | Sweden, Hallstahammar | 1993-10-14 | -- | 1993–2006 | 2 | |
| Hallstavik | Hallstavik | Sweden, Hallstavik | 1989-12-07 | 1989-12-07 | 1989 | 1 | |
| Hallunda | Hallunda | Sweden, Hallunda | 1990-10-29 | 1991-11-05 | 1990–1993 | 5 | |
| Halmstad | Halmstad | Sweden, Halmstad | 1952-03-21 | -- | 1952–1967 | 2 | |
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