A skyscraper one mile high, a dome covering most of downtown Manhattan, a triumphal arch in the form of an elephant: some of the most exciting buildings in the history of architecture are the ones that never got built.

These are the projects in which architects took materials to the limits, explored challenging new ideas, defied conventions, and pointed the way towards the future. Some of them are architectural masterpieces, some simply delightful flights of fancy. It was not usually poor design that stymied them – politics, inadequate funding, or a client who chose a ‘safe’ option rather than a daring vision were all things that could stop a project leaving the drawing board.

These unbuilt buildings include the grand projects that acted as architectural calling cards, experimental designs that stretch technology, visions for the future of the city, and articles of architectural faith. Structures likeBuckminster Fuller’s dome over New York or Frank Lloyd Wright’s mile-high tower can seem impossibly daring. But they also point to buildings that came decades later, to the Eden Project and the Shard.

Some of those unbuilt wonders are buildings of great beauty and individual form like Etienne-Louis Boullée’s enormous spherical monument to Isaac Newton; some, such as the city plans of Le Corbusier, seem to want to teach us how to live; some, like El Lissitsky’s ‘horizontal skyscrapers’ and Gaudí’s curvaceous New York hotel, turn architectural convention upside-down; some, such as Archigram’s Walking City and Plug-in City, are bizarre and inspiring by turns. All are captured in this magnificently illustrated book.