1989 Asymptote won international recognition for their winning entry of the Steel Cloud in the Los Angeles Westcoast Gateway Competition. In 1992, Lise Anne Couture and Hani Rashid were asked by The New York Times to design a hypothetical building for Times Square.
In 1996, Asymptote built their first project overseas, the Universe Theatre in Aarhus, Denmark. The project was awarded the Danish building of the year award by the Architects' Association of Denmark. In 1999, Asymptote designed the first large-capacity virtual reality environment and also completed the Advanced Floor Operations Center on the trading floor of the Wall Street facility. The project was listed in the AIA Guide to Noteworthy Architecture in New York City.
In 2003, Asymptote finished the American flagship store for Carlos Miele. Three years later, they built the AlessiFlagship Store. Both projects won the AIA NY Chapter Interior Architecture Award. In 2006, the second Carlos Miele Store opened its doors in Paris.
In November 2009, the firm completed the Yas Viceroy Abu Dhabi Hotel in Abu Dhabi, United Arab Emirates and in early 2010 166 Perry Street a luxury residential building in Manhattan's West Village was completed.
Other projects include 190 Váci Commercial Towers in Budapest, Hungary, the FCD Yongsan Landmark Tower in Seoul, South Korea, a design for the Zurich Circle, Zurich, Switzerland, the Strata Tower  an innovative, forty-story, luxury residential tower in Abu Dhabi,United Arab Emirates, a large-scale cultural, hotel and performing arts complex in Penang, Malaysia  and a commission to build the World Business Center Busan in Busan, South Korea. The design for the World Business Center Busan consists of three separate, tapered towers "soaring" out of a single base and will, upon completion, will be among the tallest buildings in Asia at 560 m.
2011 Asymptote Architecture won second place in the 'Kaohsiung Port Terminal 2010' competition, featuring a sculptural design for the Kaohsiung Port Terminal in Taiwan. Another project from 2011 was the Beukonhof, an auditorium / crematorium in the city of Schiedam, Netherlands.
In June 2012 Asymptote announced the launch of the Velo Towers, part of the Dreamhub development in the Yongsan District of Seoul, South Korea. Asymptote’s project is designed as an integral part of the master plan accommodating several new projects that are situated along the newly planned Yongsan Park.
Installations & Exhibitions
For nearly two decades, Hani Rashid and Lise Anne Couture have also produced experimental art installations and exhibition design work involving multi-media technologies such as the Virtual Museum at the Solomon R. Guggenheim Museum in New York City.
DOCUMENTA XI in Kassel, Germany; the Schirn Kunsthalle Frankfurt and the Ministry of Public Works in Madrid, Spain. In 2003, Asymptote held its first extensive solo show, a survey of its work at the Netherlands Architecture Institute (NAI). 
In 2000 Hani Rashid co-represented the United States at the Seventh Venice Biennale of Architecture, and in 2004 both Rashid and Couture were chosen as the design architects for Metamorph, the Ninth Venice Architecture Biennale. Asymptote has also produced design work, brand identities and product design for Alessi Italy, Volkswagen Wolfsberg Germany and Carlos Miele Brazil. The work of Asymptote is also included in several private and public collections including The Museum of Modern Art in New York, the Pinakothek der Moderne in Munich, the San Francisco Museum of Modern Art (SFMOMA), the Centre Georges Pompidou in Paris, and the Frac Centre in Orléans, France.
Asymptote’s work has been the subject of 4 monographs and is widely published internationally in professional journals as well as the general press.
- Hani Rashid, Lise Anne Couture: Asymptote. Architecture at the Interval, Rizzoli 1995, ISBN 0847818616
- Hani Rashid, Lise Anne Couture: Asymptote: Flux, Phaidon Press 2002, ISBN 0714841722
- Hani Rashid, Lise Anne Couture: Asymptote: Works and Projects, Skira 2002, ISBN 888491261X
- Hani Rashid, Lise Anne Couture: Asymptote Architecture Actualizations, Asia Art & Design Cooperation 2010, ISBN 978-7-5609-5599-5
Redesigning the World
Newsweek, Cathleen McGuigan, 2009
Strata Tower, Architectural Design
vol. 79, no. 2, 2009
Specifier, no. 78, Alys Moody, 2008
The Virtual Messiahs
Whitewall, Aric Chen, 2008
New Directions in Contemporary Architecture
John Wiley & Sons Ltd., 2008
Modern Architecutre A-Z
Architectural Design, vol. 77, no. 1, 2007
A Luxury Condo by Arty Architects from the Fringe
The New York Times, Arts Section, June 28, 2007
Vol. 4, Taschen, 2006
Rem Koolhaas + Hani Rashid
The Architect’s Newspaper, October 6, 2006
Design Document Series 09: Scape_Asymptote Architecture/USA
DAMDI Co., Ltd, 2004
Architecture Now 3: The Architecture of Today
On the Road to Venice: 9th Architecture Biennale
Architectural Record, Robert Ivy, 2004
Thoughts on the Metamorphoses of Architecture
Log, Kurt Forster. Fall 2004
A + U, July 2004
Architectural Laboratories: Greg Lynn & Hani Rashid
NAi Publishers, 2002
Phaidon Press, 2002
Haarlemmermeer Pavilion by Asymptote: Hydrapier
The Rashid Machine
Metropolis, Peter Hall, 2001
Curves Ahead: What About Blobs
Details, James S. Russell, Michael Moran, 2001
Reinventing the Museum
Wired, Jessie Scanlon, Carolyn Rauch, David Jang, 2000
Guggenheim Virtual Museum
Asymptote: Rashid + Couture
Asymptote’s Dual Projects for the NYSE
Architectural Record, Sarah Amelar, 1999
Architecture in the 1990s
New Forms, Philip Jodido, ed., Taschen, Cologne, 1997
Architecture for the Future, Pierre Terrall Editions, Paris, 1996
Asymptote: Architecture at the Interval
Rizzoli International Publications, 1995
- Middle East Architect Awards, Hospitality Project of the Year, The Yas Hotel (2011)
- Travel + Leisure Design Awards, Best Large Hotel, The Yas Hotel (2010)
- Grand Prix de l'Architecture, Festival Automobile International (2010)
- IESNA Illumination Award (2010)
- Le Grand Prix de l’Architecture, FAI, Paris, The Yas Hotel (2010)
- American Architecture Award, Chicago Athenaeum Museum of Architecture and Design (2008)
- AIA NY Chapter Design Award, Interior Architecture (2007)
- AIA New York Chapter Design Award, Interior Architecture (2005)
- Frederick Kiesler Prize for Architecture and the Arts (2004)
- AIA New York Chapter Design Award, Architecture (2002)
- Muschamp, Herbert (November 1, 1992). "Architecture View; Time to Reset the Clock in Times Square". The New York Times. Retrieved 23 January 2010.
- Luscombe, Belinda (8 September 2003). "Building Momentum". Time.com. Retrieved 5 January 2008.
- "Project Portfolio: HydraPier". Architectural Record. Retrieved 7 January 2008.
- "Entering a Dream Landscape (But, Really, It's a Store)". The New York Times. 12 June 2003. Retrieved 8 January 2008.
- "Asymptote 3.0". Metropolis Magazine. Archived from the original on 16 December 2007. Retrieved 7 January 2008.
- "Commendable Achievement: Interior Lighting". Architectural Lighting. Retrieved 7 January 2008.
- "The Yas Hotel". December 2009. Archived from the original on 2010-11-19. Retrieved 29 June 2013.
- Pogrebin, Robin (28 June 2007). "A Luxury Condo by Arty Architects From the Fringe". The New York Times. Retrieved 5 January 2008.
- "Asymptote’s FCD Yongsan Tower in Seoul". http://www.evolo.us. 22 May 2010.
- "the-circle-at-zurich-airport-by-asymptote-architecture". 24 May 2010.
- "strata-tower-by-asymptote". Dezeen.com. 13 May 2008.
- "the-strata-tower-by-asymptote.html". Designboom.com.
- "Asymptote to Spice Up Penang's Skyline". Architectural Record. Archived from the original on 31 January 2008. Retrieved 7 January 2008.
- "A Global City Center". worldarchitecturenews.com. 21 September 2007.
- "Asymptote wins competition for WBCB Tower". Architectural Record. Retrieved 7 January 2008.
- "Asymptote Building Big in Asia". Architectural Record. Retrieved 5 January 2008.
- "Asymptote Architecture secures second place in Kaohsiung Port Terminal Competition". WIDN News. 22 December 2010.
- "Beukenhof Auditorium". http://www.architizer.com.
- "velo-tower-by-asymptote". Dezeen.com. 14 June 2012.
- "ASYMPTOTE ANNOUNCES VELO TOWERS IN SEOUL, SOUTH KOREA". http://www.asymptote.net.
- Hales, Linda (Mar 11, 2006). "A Curate-Your-Own Museum Web Site". The Washington Post (Washington, D.C.). pp. C.02. Retrieved 23 January 2010.
- "approach the future - the asymptote experience". designboom.com.