From traditional Japanese stacked sandals to weird rubber creations by Zaha Hadid and Prada tongues in flames, high-heeled shoes tower provocatively above all other footwear in women’s – and men’s – imaginations. A new exhibition traces their first steps in the 16th century through to modern designers’ erotic flights of fancy

• Killer Heels is at Brooklyn Museum, New York, from 10 September to 15 February 2015