Crenshaw, or the Crenshaw District, is a neighborhood in South Los Angeles, California. In the post–World War II era, a Japanese Americ…Crenshaw, or the Crenshaw District, is a neighborhood in South Los Angeles, California. In the post–World War II era, a Japanese American community was established in Crenshaw. African Americans started migrating to the district in the mid 1960s, and by the early 1970s were the majority.