Following the passing of the National Art Gallery and Dominion Museum Act in 1930, the two institutions shared a single board of trustees.

[7] The early holding consisted largely of donations and bequests, including those from Harold Beauchamp, T. Lindsay Buick, Archdeacon Smythe, N. Chevalier, J. C. Richmond, William Swainson, Bishop Monrad, John Ilott and Rex Nan Kivell.

Shed 11 the Temporary/Contemporary was situated on the Wellington waterfront in a converted industrial warehouse built in 1905[9] and exhibited contemporary art, both local and international, until 1992.

[12] The official opening took place on 14 February 1998, in a ceremony led by Prime Minister Jenny Shipley, Sir Peter Blake, and two children.

[15] The main Te Papa building is built on reclaimed land on Cable Street which formerly belonged to the Wellington Harbour Board.

Board members have included: Wira Gardiner, Fiona Campbell, Sue Piper, Judith Tizard, John Judge, Miria Pomare, Michael Bassett, Christopher Parkin, Sandra Lee, Ngātata Love, Ron Trotter, Glenys Coughlan, Judith Binney, Philip Carter, Wendy Lai[27] and Api Mahuika.

Until 1992 these antiques were displayed in period rooms at the Dominion Museum, and objects from the Elgar Collection are currently exhibited throughout Te Papa.

The hands-on and interactive exhibitions focus on engaging young visitors and include out-door areas built and planted for Te Papa.

[47] Te Papa charges an entrance fee of $35 for international visitors (as of September 2024) however it remains free entry for all New Zealanders.

The library is a major research and reference resource, with particular strengths in New Zealand, Māori, natural history, art, photography and museum studies.

The siting of significant collections at the water's edge on reclaimed land next to one of the world's most active faults has resulted in concern by some people.

[58] New Zealand art commentator Hamish Keith, a member of the board that set up the Museum of New Zealand and a member of its interim board,[59] has been a consistent critic of Te Papa at different times referring to it as a "theme park", the "cultural equivalent to a fast-food outlet" and "not even a de facto national gallery",[60] but seemed to moderate his opinion later when making a case for exhibition space on the Auckland waterfront.

[66][67][68] Numerous museum experts and scientists in New Zealand and worldwide criticised the move, with researchers including Steve O'Shea advocating a boycott.

[79][80][81] Between April and May 2019, Te Papa advertised a research position for a molluscan curator and awarded the job to an alternative candidate to Bruce Marshall.

They threatened to take Te Papa to court on the grounds of "blasphemous libel", a 1961 Crimes Act offence against "religion, morality and public welfare".

The move sought to align Te Papa with other art museums that have taken the side of artistic freedom in spite of well publicised protest (the statuette was banned in Adelaide, stolen in Sydney, and dropped from its British tour).

[89] The leader of the Christian Heritage Party claimed that the sacrilegious display of the statuette was hypocritical, given that the museum is careful not to offend sensitivities about Māori spirituality.

[92] Curator Ian Wedde also undertook to consider a more cautious approach with contemporary art exhibitions, ‘In future, we may have to say there's a risk management factor to consider.

'[93] Advice for pregnant and menstruating women to avoid a behind-the-scenes tour of some of Te Papa's collections in 2010 had some questioning if this was appropriate inclusiveness for a national museum.

A Te Papa spokeswoman at the time said the policy was in place because of Māori beliefs surrounding the taonga collection included in the tour "for their own safety".

[85] Taranaki tribal elders raised objections to a 19th-century Te Papa-owned painting that the museum planned to lend to the Govett-Brewster Art Gallery in New Plymouth in 2019.

Te Papa said it hoped the piece, View of Mt Egmont, Taranaki, New Zealand, taken from New Plymouth, with Maoris driving off settlers' cattle, painted by William Strutt, would spark a conversation about historical perspectives.

[98] Te Papa spokeswoman Kate Camp also told Stuff that the bottles had been created for display purposes only and were not samples.

Te Papa head of art Charlotte Davy said the museum would be making warning signs more obvious and installing new ones.