1989 Asymptote won international recognition for their winning entry of the Steel Cloud in the Los Angeles Westcoast Gateway Competition. In 1992, Asymptote was invited 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 for the New York Stock Exchange as well as the construction of 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 Awards. In 2006, the second Carlos Miele Store also designed by Asymptote opened its doors in Paris.
In November 2009, Asymptote 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 Budapest Bank 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
In the early years of the practices, Asymptote 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 Asymptote was 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, Curated and edited by Bruce Q. Lan,United Asia Art & Design Cooperation (AADCU) 2010, ISBN 978-7-5609-5599-5
- Redesigning the World, Newsweek, Cathleen McGuigan, 2009
- Strata Tower, Architectural Design, vol. 79, no. 2, 2009
- Architectural Iconoclasts, 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, Taschen, 2008
- Performing Elegance, 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
- Architecture Now!, 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, Taschen, 2004
- On the Road to Venice: 9th Architecture Biennale, Architectural Record, Robert Ivy, 2004
- Thoughts on the Metamorphoses of Architecture, Log, Kurt Forster. Fall 2004
- Asymptote, A + U, July 2004
- Architectural Laboratories: Greg Lynn & Hani Rashid, NAi Publishers, 2002
- Flux, Phaidon Press, 2002
- Haarlemmermeer Pavilion by Asymptote: Hydrapier, BIS, 2002
- 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, Domus, 2000
- Asymptote: Rashid + Couture, A+U, 1999
- Asymptote’s Dual Projects for the NYSE, Architectural Record, Sarah Amelar, 1999
- Architecture in the 1990s, New Forms, Philip Jodido, ed., Taschen, Cologne, 1997
- Asymptote Architecture, 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. External link in
- "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.[permanent dead link]
- "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. Archived from the original on 2010-12-24.
- "Beukenhof Auditorium". http://www.architizer.com. External link in
- "velo-tower-by-asymptote". Dezeen.com. 14 June 2012.
- "ASYMPTOTE ANNOUNCES VELO TOWERS IN SEOUL, SOUTH KOREA". http://www.asymptote.net. External link in
- 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. Archived from the original on 2011-11-13.