The advent of network functions virtualization (NFV) has revolutionized numerous network-based applications due to its several benefits such as flexibility, manageability, scalability, and security. By the software-based virtualization of network functions on a single infrastructure, NFV provides users with a framework that dynamically provisions various network services in a flexible manner. However, NFV faces several security challenges (e.g., multi-tenancy and live migration) which make it vulnerable to some cybersecurity attacks (e.g., side-channel attacks and shared resource misuse attacks). In this paper, we provide an overview of NFV, discuss potentially serious security threats on NFV and introduce effective countermeasures to mitigate those threats. Finally, we suggest some practical solutions to provide a trustworthy platform for NFV. (C) 2016 Elsevier B.V. All rights reserved.