In September 1988, during the 20th anniversary celebration of Evergreen Marine Corporation's founding, company chairman Chang Yung-fa announced his company's intentions to establish Taiwan's first private international airline. The opportunity to create a major Taiwanese airline had just arisen following a decision by the Taiwanese government to liberalise the country's air transportation system. 

Upon receipt of regulatory approval, EVA Airways Corporation was formally established in March 1989. The airline was originally to be called Evergreen Airways,however this was too similar to the unrelated Evergreen International cargo airline. In October 1989, the newly formed EVA Airways Corporation placed an order for 26 aircraft from Boeing and McDonnell Douglas, including Boeing 747-400 and MD-11 airliners. Pronounced "E-V-A Air", of which "EVA" stands for Evergreen Airways, based its operations at Taoyuan International Airport near Taipei, Taiwan.

Operations began on 1 July 1991 with a small fleet of Boeing 767-300ER. Initial destinations from Taipei were Bangkok, Seoul, Jakarta, Singapore, and Kuala Lumpur.

In 1992, EVA Air received the first of its Boeing 747-400 aircraft on order, and launched its premium economy class, "Economy Deluxe", on its 747 transpacific flights to Los Angeles. EVA Air's premium economy cabin was the first in the world, featured a wider 2-4-2 abreast configuration. In 1993, EVA Air added flights to London, Paris, Seattle, New York, San Francisco,Sydney, Bangkok and Vienna with the Boeing 747-400, as well as, other East Asian destinations with the rest of the fleet. 

In 1994, purchased a total of eight more aircraft, including three MD-11s, one Boeing 747-400 and four Boeing 767-200s. The airline also added Hawaii, Bali, Fukuoka and Auckland routes to its network.

Dedicated EVA Air Cargo operations began in April 1995, with the first weekly McDonnell Douglas MD-11 freighter flights to Taipei, Singapore, Penang, San Francisco, New York, and Los Angeles. 

In the mid–1990s, EVA Air expanded into the domestic Taiwan market by acquiring shares in Makung International Airlines, followed by Great China Airlines and Taiwan Airways. On 1 July 1998, all three carriers, as well as EVA's existing domestic operations, merged under the UNI Air title. UNI Air became EVA Air's domestic intra-Taiwanese subsidiary, operating short haul flights out of its base in Kaohsiung, Taiwan's southern port and second-largest city. it operated with a fleet of McDonnell Douglas MD-90-30 (photo below),Bombardier Dash 8-Q200/300 and BAe 146-300. 

In 2000, EVA Air embarked on its first major long-haul fleet renewal. The airline became one of the launch customers for the Boeing 777-300ER, ordering four aircraft. In January 2001, EVA Air ordered its first Airbus aircraft, the A330-200 which it took delivery on June 26, 2003. It also introduced its new generation of a top cabin class, Premium Laurel, along with an upgraded economy class and a new state-of-the-art Audio/ Video on Demand system.

In 2004, EVA Air converted its remaining eight options for Boeing 777-300ERs into firm orders. The first Boeing 777-300ER entered service as EVA Air's new flagship aircraft in July 2005 serving the Taipei-Bangkok-London route. 

In 2007, EVA Air announced a nonstop Taipei to New York, to be operated with its new long-range Boeing 777-300ERs. However, in 2008, the airline also announced the suspension of services to Auckland as the company reported losses earlier that year. The carrier also prepared to increase direct flights to China, after initiating weekly charter flights in July 2008 following changes to the Three Links travel agreements with the chinese mainland.

In August 2010, EVA Air was named one of the top 10 international airlines in Travel+Leisure's World's Best Awards. In 2010, EVA Air started services to Toronto, which began on 29 March 2010. In mid-2011, EVA Air announced plans to acquire further 777-300ERs to complete the replacement of its 747-400 aircraft on Europe and U.S. routes, along with A321 series narrow-body jets to replace its MD-90 fleet.On 27 March 2012, EVA Air announced that it would join Star Alliance in 2013, becoming a full member on 18 June 2013. 

In October 2014, EVA AIR announced to expand its North American network by adding new routes to Houston in 2015 and Chicago in 2016, along with expanding 55 flights per week to 63 flights per week to North America. The Houston route launch will be complemented by the introduction of the seventh and last Hello Kitty jet, Kikilala-themed "Shining Star" Boeing 777-300ER.

In October 2015, EVA AIR announced its intent to purchase up to 24 Boeing 787 Dreamliners and two additional 777-300ER from Boeing to continue to place itself as one of the most modern carries in the Asian region with an excellent safety and service level. Therefore it was nominated several times with the Skytrax 5 Star recognition award. In November 2015, Eva Air unveiled a new livery on their 22nd 777 along with new boarding music and improved service on board. 

In January 2016, Evergreen Group chairman Chang Yung-fa died, leaving control of the company to his son by his second marriage, Chang Kuo-Wei. However he was removed by a coup by the three children of Chang Yung-fa's first marriage and replaced with Lin Pang-Shui (Steven Lin). 

On 24 August 2017, EVA Air unveiled their third-generation uniform. On 2 October 2018, EVA Air took delivery of their first of four Boeing 787-9 Dreamliners. The airline also has orders for 20 787-10s and options for six more. In June 2019, the first of the initial 787-10 started to arrive at its Taipei base. 

History source: Wikipedia.org + EVA Air