Network slicing is a technique for flexible resource provisioning in future wireless networks. With the powerful SDN and NFV technologies available, network slices can be quickly deployed and centrally managed, leading to simplified management, better resource utilization, and cost efficiency by commoditization of resources. Departing from the one-type-fits-all design philosophy, future wireless networks will employ the network slicing methodology in order to accommodate applications with widely diverse requirements over the same physical network. On the other hand, deciding how to efficiently allocate, manage, and control the slice resources in real time is very challenging. This article focuses on the algorithmic challenges that emerge in efficient network slicing, necessitating novel techniques from the communities of operation research, networking, and computer science.