The PUMA Basket sneaker first came on the scene in the 1960s as a basketball warm-up shoe. It gained new traction a few decades later to help define the emerging hip-hop look. Now it's rising even higher on a chunky platform with a slight slope and a ridged bumper toe-all while retaining its retro roots and its timeless PUMA styling. Style Name: Puma Basket Platform Sneaker (Women). Style Number: 5262976 4. Available in stores.