Although the word “pump” is likely derived from the French word “pompe,” which in 16th-century France was the word for a low shoe worn mostly by men, the pump as we know it today is generally used to describe a slip-on shoe with a rounded or V-shaped throat. Most pumps have heels that are at least moderately high, but the toes of pumps can be round, come to sharp points, or even remain open.

While some pumps rest on relatively modest heels, many people think of pumps and high heels in the same breath. Because a pump’s throat is uninterrupted by Mary Jane-like buckles, t-straps, or even ankle straps, they have a clean, business-wear look. That’s why a good pair of pumps can give a professional woman a commanding and empowering presence in a meeting or interaction with colleagues. Then, back at her desk, she can easily kick off her shoes to give her dogs a rest.

The shapes of pumps can vary, but the classic profile was codified in the 1950s by companies such as Gina in London (named by shoemaker Mehmet Kurdash after his muse, Gina Lollobrigida) and designers like Roger Vivier and Salvatore Ferragamo. Up front the toe comes to a point. In the back, echoing the toe’s geometry, the heel tapers quickly. The outside of the shoe is often monochromatic, constructed from shiny patent leather, mysterious black satin, and soft, elegant suede...