A wave of start-up companies is looking to tap into a lucrative market—weary parents—by creating babysitting services for the digital age. Kinderfee, a German website that operates across Europe, provides parents with a database of thousands of potential sitters who have been interviewed and screened by the company, and helps arrange meetings between parents and prospective sitters. (A fee is then included in the babysitter’s bill.) In the United States, the website Urban Sitter features profiles, ratings and reviews of local babysitters, and also links with Facebook to help parents refer babysitters to friends. But the benefits of high-tech babysitting don’t have to end when parents leave for the night. Apps like Babysitter Log allow sitters to tell parents what their children are up to throughout the night—and in some detail. Sitters can indicate if the children are playing or sleeping, or can use a drop-down menu to update parents on the results of the latest diaper change.