The advent of 5G and the ever increasing stringent requirements in terms of bandwidth, latency, and quality of service pushes the boundaries of what is feasible with legacy Mobile Network Operators’ technologies. Network Functions Virtualization (NFV) is a promising attempt at solving some of these challenges that is widely adopted by the industry and specified by the standardization bodies. In essence, NFV is about running nf as virtualized workloads on commodity hardware. This may optimize deployment costs and simplify the lifecycle management of nf, but it introduces new fault management challenges and issues. In this paper, we propose a comprehensive state of the art of fault management techniques. We address the impact of virtualization in fault management. We propose a new classification of the recent fault management research achievements in the network virtualization environments and compare their major contributions and shortcomings.