These topics come together in the case of Nike’s white-on-white Air Force 1, named after the president’s airplane. The shoe, introduced in 1982 and discontinued a year later, was reintroduced in 1986. It “was touted as the sneaker of choice for drug dealers, whose ability to wear unscuffed sneakers signified both wealth and status,” Ms. Semmelhack writes.

In 1984, Nike’s Peter Moore designed the first Air Jordans and the “jumpman” logo for Michael Jordan, then a rookie with the Chicago Bulls. The sneakers’ red and black colors violated N.B.A. uniform regulations at the time, but Jordan wore them anyway, incurring a $5,000 fine for every game he played in them. He became a role model of antiauthoritarian individualism, which was great advertising for Nike. The company happily paid Jordan’s penalties, and the shoes sold “like Cabbage Patch dolls,” a Nike spokesman said.

Then, in the late 1980s, came a beautifully produced series of TV commercials for Air Jordans directed by Spike Lee and starring Jordan, with Mr. Lee playing Mars Blackmon, his character from his film “She’s Gotta Have It.” Controversy ensued as cases of killings seemingly linked to people stealing sneakers from their wearers started appearing in the news media. An article in The New York Post, Ms. Semmelhack writes, “put the blame for recent sneaker killings squarely at the feet of Nike, Michael Jordan and Spike Lee.” Mr. Lee called the article racist, and the debate raged on. In 2004, Bill Cosby weighed in with his infamous “Poundcake” speech, in which he called out supposedly irresponsible parents of young blacks in harsh language. Ms. Semmelhack quotes him: “They’re buying things for the kid. $500 sneakers, for what? They won’t buy or spend $250 on Hooked on Phonics.”

But perhaps the most intriguing point Ms. Semmelhack makes in the catalog is that “young African-American men weren’t so much being advertised to as they were being advertised through.” A news release put out by the British Knights footwear company in the mid-80s declared that “the only way to get a middle-class suburban high school kid to buy your product is to have an inner-city kid wear it.” Ms. Semmelhack asks: “What was being gained by promoting the sneakers’ association with inner-city street culture, including violence? What was being gained by this association with high-achieving black athletes? The answer was authenticity.”

Today there’s an international culture of collecting that has “sneakerheads” acquiring rare, vintage models for extraordinary sums. That’s yet another dimension of sneaker culture that cries out for more penetrating consideration. A chapter in the catalog instructing collectors on how to care for their treasures by Ada Hopkins, the Bata Shoe Museum’s conservator, is less than illuminating in that regard. Sneakerheads probably won’t mind, though. For them, the exhibition should be catnip.