Nike’s new Vaporfly running shoes are so good that they were nearly banned from the next Olympics. These super-performance shoes aren’t the only new sneakers that might deserve a place in your closet. Here’s a look at innovative shoes for a range of activities… 

Running: Nike ZoomX Vaporfly Next%. Vaporflys are a source of debate in the competitive track world. They boost running speeds by 4% to 5%, which critics consider an unfair advantage. But if your goal is to run faster or farther, there’s no debate—they’re the best running shoes on the market. Vaporflys have a carbon fiber plate hidden inside the thick foam padding underfoot. This acts like a catapult, springing the runner forward subtly with each stride, increasing speeds while ­reducing leg ­fatigue. $250. 

Cross-training: Vivobarefoot Stealth III. The growing consensus among fitness pros is that less is more with cross-training shoes. Less foam underfoot and a relatively flat base means more stability thanks to better sensory feedback from the nerves and joints of the feet. A less constraining “toe box” lets the toes spread out, further improving balance. Vivobarefoot is the “minimalist” shoe ­expert—the ultra-flexible Stealth IIIs are like gloves for the feet. $101. ­

Walking: Nike Free RN 5.0. Current thinking is that walking shoes should find a middle ground between minimalist footwear and thick-soled running shoes. These Nikes, which the company calls a running shoe, are a well-made example of that. They’re a reasonable choice for short runs, too. $50 to $100.

Off-road running: La Sportiva Wildcat. Like off-road tires for your feet, these trail-running shoes have thick, grippy treads for traction on dirt, grass and gravel—without the weight and limited ankle flexibility of hiking boots. The sole provides both cushioning and stability. They are great for light hikes, too. $110.

Biking: Vans Old Skool. Unlike the other shoes on this list, these Vans are not new and innovative—they’re named “Old Skool” for a reason. What’s new is that these venerable sneakers are increasingly popular for casual bike rides. Originally designed for skateboarders, their wide, level, grippy, stiff soles are ideal for maintaining control of bike ­pedals. Unlike cycling cleats, they’re comfortable for walking when you get off the bike. $60.