No wonder many business leaders live in a heightened state of alert. Thanks to outsourced cloud infrastructure, mix-and-match technology components, and a steady flood of venture money, start-ups and established attackers can bite before their victims even see the fin. At the same time, the opportunities presented by digital disruption excite and allure. Forward-leaning companies are immersing themselves deeply in the world of the attackers, seeking to harness new technologies, and rethinking their business models—the better to catch and ride a disruptive wave of their own. But they are increasingly concerned that dealing with the shark they can see is not enough—others may lurk below the surface.