It is a common sneer against avant-garde architects that most of their work exists only on paper. But if that's supposed to be an insult, consider the extraordinary, paper-based career of Giovanni Battista (or Giambattista) Piranesi (1720–1778). Born near Venice and trained in the building arts by his uncle, a master architect and engineer, the ambitious Giambattista headed to Rome at the age of 20—just as a major construction boom was tapering off. One way the young architect could support himself through the downturn was by producing vedute, or views, of the city as tourist souvenirs. Inspired by the “speaking ruins” all around him—eloquent, tantalizing fragments of the classical past—Piranesi took up chalk and pen and began to compose dramatic architectural scenes of Rome, infused with his knowledge of archaeology and ancient history (Piranesi was an accomplished antiquarian), but more important, by his rich, almost febrile, imagination.

Piranesi gained fame with the 135 vedute he printed from the 1740s through the 1770s. These etchings, which exaggerate the grand scale and crumbling decay of Rome's ancient monuments, helped establish the Romantic image of the city that persisted in Europe through the 19th century (Lord Byron, for instance, evoked a Piranesian Rome—a dark, overgrown “chaos of ruins”—in his wildly popular poem “Childe Harold's Pilgrimage”). Piranesi's Carceri d'Invenzione (“Imaginary Prisons”), 16 surreal depictions of cavernous interiors with bizarre machinery and endlessly repeating staircases and arches, hold a strong appeal today for viewers schooled in science fiction and M.C. Escher.

Less well known, however, than Piranesi's work as a graphic artist is his work as a designer of architecture, interiors, and furnishings. As early as his formative years in Venice, Piranesi was starting to develop an idiosyncratic, profusely Baroque style as a rebuke to the current fashion for ornamental restraint. In his designs for side tables and chimneypieces, candelabra and church altars, fantastic capricci emerge from mingled Roman, Greek, Etruscan, and Egyptian motifs. At the root of this eclecticism, writes his biographer John Wilton-Ely, lay “Piranesi's belief in the prerogative of the designer's imagination.”

A new exhibition at the Cooper-Hewitt Museum in New York will shed light on this neglected aspect of Piranesi's legacy. Opening Sept. 14, “Piranesi as Designer,” curated by Wilton-Ely and by Sarah Lawrence, includes more than 100 etchings, original drawings, and decorative objects by Piranesi, as well as works by contemporary architects like Peter Eisenman and Robert A.M. Stern, who continue to feel Piranesi's pull. On the pages that follow, ARCHITECT presents highlights from the show.