Network functions virtualization (NFV) is a new network architecture framework where network function that traditionally used dedicated hardware (middleboxes or network appliances) are now implemented in software that runs on top of general purpose hardware such as high volume server. NFV emerges as an initiative from the industry (network operators, carriers, and manufacturers) in order to increase the deployment flexibility and integration of new network services with increased agility within operator's networks and to obtain significant reductions in operating expenditures and capital expenditures. NFV promotes virtualizing network functions such as transcoders, firewalls, and load balancers, among others, which were carried out by specialized hardware devices and migrating them to software-based appliances. One of the main challenges for the deployment of NFV is the resource allocation of demanded network services in NFV-based network infrastructures. This challenge has been called the NFV resource allocation (NFV-RA) problem. This paper presents a comprehensive state of the art of NFV-RA by introducing a novel classification of the main approaches that pose solutions to solve it. This paper also presents the research challenges that are still subject of future investigation in the NFV-RA realm.