Network functions virtualization is an emerging technology that can significantly improve the flexibility of network service provisioning and offer potential cost savings. However, it is critical that service providers offer high reliability and availability of the network and services when moving from proprietary hardware appliances to virtualized network functions on commodity servers. In a network consisting of physical appliances, providers can deploy redundant hardware and extra capacity to handle failures, although this is quite expensive in practice. Virtualization of network functions lead to more challenges for resiliency, but also bring new opportunities to address these challenges in a more cost-effective manner. In this article, we explain the resiliency requirements for virtual network functions in order to provide carrier grade services, summarize the existing solutions in the literature, highlight several research challenges, and present a concrete case study to demonstrate how to decompose a type of virtual router and thus enhance its resiliency.