Apoorva Mehta is the CEO of Instacart, a nearly year-old grocery delivery service that has already raised $2.3 million. For just $4 plus tip–roughly the price of a cup of Blue Bottle’s finest drip–Instacart customers can order food online from a handful of grocery stores, including Trader Joe’s and Whole Foods, and send a “personal shopper” (that is to say, a delivery guy) to bring it to their door in three hours or less. Urban food-delivery startups are nothing new–Webvan and Kozmo.com managed to burn half a billion dotcom dollars between them before going bust in 2001–but Mehta’s company takes advantage of two peculiar things about cities in 2013: the ubiquity of smartphones and persistently high underemployment. Instacart’s personal shoppers are independent contractors paid on commission. The average wage is between $12 and $15 an hour. The contractors use their own mobile devices and vehicles.

Read more about Apoorva at Fast Company

Before doctors do anything, they have to check a patient’s insurance coverage. These checks cost millions and use “armies of people making phone calls,” says Katelyn Gleason, whose solution is the startup Eligible. It offers one-stop online insurance verification for doctors.

Read more about Katelyn at Fast Company

Mahbod Moghadam started Rap Genius (1) in 2009 as a way to solve a dispute with his friend and cofounder, Tom Lehman, over a lyric on rapper Cam’ron’s album Purple Haze. (2) Then Moghadam had a vision: “I kid you not, Jesus came down and told me that Rap Genius is going to be the biggest website in the world,” he says. 

Read more about Mahbod at Fast Company