Nanotechnology and nanomaterials have offered sustainable design options for the built environment and enabled architects to design more flexible architectural forms. Carbon nanotubes have excellent mechanical, electrical, thermal, and chemical properties and are useful in a wide range of engineering applications. However, the role of carbon nanotube composites as a functional construction material has large potential and awaits further investigation and exploration. This paper gives an overview of the synthesis and fabrication methods of carbon nanotubes, carbon nanotube properties, different forms of carbon nanotube composites, and application of carbon nanotubes in the construction industry. To explore the prospects for construction use, the aesthetic, structural, and functional characteristics of several futuristic building projects are discussed. This overview proposes a promising material approach for the application of carbon nanotubes in construction and explains the related opportunities and challenges.