The fifth generation of mobile communications is anticipated to open up innovation opportunities for new industries such as vertical markets. However, these verticals originate myriad use cases with diverging requirements that future 5G networks have to efficiently support. Network slicing may be a natural solution to simultaneously accommodate over a common network infrastructure the wide range of services that vertical-specific use cases will demand. In this article, we present the network slicing concept, with a particular focus on its application to 5G systems. We start by summarizing the key aspects that enable the realization of so-called network slices. Then, we give a brief overview on the SDN architecture proposed by the ONF and show that it provides tools to support slicing. We argue that although such architecture paves the way for network slicing implementation, it lacks some essential capabilities that can be supplied by NFV. Hence, we analyze a proposal from the ETSI to incorporate the capabilities of SDN into the NFV architecture. Additionally, we present an example scenario that combines SDN and NFV technologies to address the realization of network slices. Finally, we summarize the open research issues with the purpose of motivating new advances in this field.