[3][4] The Copen was originally designed with a 660 cc turbocharged engine in order to meet Japanese kei car regulations.

[citation needed] The leading characteristic of this model was the active top, a motorized hide-away hard roof.

[13] The Copen has been featured on the UK show Top Gear where James May attempted to find the best convertible car.

On 13 January 2011, Daihatsu announced that it would withdraw the Copen from the European market in 2011 due to the increasing strength of the Japanese Yen and sharp decline in sales from 2006 to 2011.

[14] Daihatsu announced on 2 April 2012 that the production for the Copen would cease in August 2012 with the final "10th Anniversary Edition" model.

[19] At the 2013 Tokyo Motor Show, Daihatsu unveiled two Copen concept cars called the Kopen, with the tagline "Future Included".

[21] The body panels are made of 13 separate resin components, 11 of which are interchangeable to modify design and colours.

Daihatsu produced a limited run of 200 units in April 2019 to coincide with the fifth anniversary of the second generation Copen.

The Vision Copen is a rear-wheel-drive concept car showcased at the 2023 Japan Mobility Show.