The first Director of the Centre was

• Ásgeir Ólafsson, who served as CEO alongside the chairman of the board until 1985, and who retired from the role of managing director in 1986.

• Geir Zoega was the Director of the Institute until 2000

• Ásgeir Ásgeirsson was the Director of the Institute until 2010

• Hulda Ragnheiður Árnadóttir has been the director of NTÍ since that time

The chairs of the board, other than Ásgeir Ólafsson, have been Einar B. Ingvarsson from 1985-1991, Guðmundur Þ. B. Ólafsson 1991-1995, Jón Ingi Einarsson 1995-2007, Torfi Áskelsson 2007-2011, Guðrún Erlingsdóttir 2011-2015 and Sigurður Kári Kristjánsson since 2015.

The main role of NTÍ is to insure buildings and movable property in Iceland against natural disasters. All buildings are insured but available assets only if they are fire-insured by the general insurance companies.

The operations of the Institute have remained largely unchanged from the beginning. The general insurance companies are responsible for collecting premiums on behalf of NTÍ, in parallel with collecting premiums for fire insurance. The insured can only be insured against direct losses caused by volcanic eruptions, earthquakes, landslides, avalanches and water avalanches. No consequential losses or losses resulting from interruption of operations following natural disasters are covered. A premium of 0.25‰ of the insurance premium equals the fire insurance amount of buildings, premises and movable property.

Since 1982, provisions have been in force requiring owners of various structures that are not customary for fire safety, such as various power and utility installations, bridges and harbours. It is not compulsory to cover these assets with the NTÍ, but owners are obliged to ensure that such insurance is available from any insurance company. It is common for the largest power companies to insure installations related to power generation, directly with foreign insurers. The premium for such construction projects is 0.2240 of the insurance amount.

NTÍ reinsures risks arising from large insurance events at international level, but at any given time between 20 and 30 foreign reinsurance companies are parties to a contract with NTÍ in connection with natural disasters.

The operations of NTÍ have been located in Hlíðasmára 14 in Kópavogur since 2014. As a rule, the Institute employs four to five permanent staff, including those in specialised projects related to risk assessment in the event of natural disasters and the development and maintenance of information systems that must always be in a position to fulfil their role in the event of major damage events.

The following are the main claims that have occurred since Iceland's Penalty Insurance was established in 1975:

• earthquake at Kópasker, 13 January 1976,

• a scramble flood in Patreksfjörður on 22 January 1983,

• tidal floods in Akranes, 5 January 1984,

• tidal flooding in Eyrarbakki, Stokkseyri and elsewhere on 9 January 1990,

• avalanche in Súðavík on 16 January 1995,

• avalanche in Flateyri on 26 October 1995,

• a jökulhlaup on Skeiðarársandur, November 4, 1996,

• earthquakes in South Iceland, June 17 and 21, 2000,

• earthquake in South Iceland on May 29, 2008,

• volcanic eruption in Eyjafjallajökull on 14 April 2010; and

• a volcanic eruption in Grímsvötn on May 21, 2011.

• avalanche in Flateyri, Iceland, on 14 January

• mudslides in Seyðisfjörður, Iceland, 15 to 18 December 2020

• avalanche in Neskaupstaður on March 27 2023

Each year, on average, seven events falling under the NTÍ insurance obligation occur, but most often they only cause damage to a few assets at a time, e.g. in floods and mudslides.