Gun violence is up across the country. It’s changing mayoral politics.

Kasim Reed wasn’t planning on running for another term as mayor of Atlanta. But rising crime and the problems that have come with it — like one of Atlanta’s wealthiest districts trying to secede from the city — pushed him out of mayoral retirement and into an already crowded race.

Homicides and shootings are up and the number of cops is down in cities from Atlanta to Seattle. Crime, as a result, is dominating the discourse in mayoral races — driving candidates to talk about beefing up police patrols and...