HAVANA — Kathleen Murphy Skolnik gasped one recent morning as she gazed up into the stairwell of a 1939 downtown apartment building here and pointed at the chevron pattern in the ironwork, at the unpolished rust-pink marble and a simple alcove on the stairway crowned by a stepped arch.

“It’s so beautiful,” said Ms. Skolnik, an architectural historian who lives in Chicago. “And it’s so run-down.”

Ms. Skolnik’s words serve as an unofficial motto for the rich, wide-ranging and often neglected buildings that, experts say, make Cuba one of the world’s most significant but overlooked troves of Art Deco architecture. As some 250 Cuban and foreign connoisseurs gathered last week in Havana for the World Congress on Art Deco, there was hope the event would foster wider recognition of the island’s Art Deco heritage and the urgent need to preserve it. (The gathering, of the World Congress of the International Coalition of Art Deco Societies, ends on Thursday.)...