The introduction of Network Function Virtualisation (NFV) represents a significant change in networking technology, which may create new opportunities in terms of cost efficiency, operations, and service provisioning. Although not explicitly stated as an objective, the dependability of the services provided using this technology should be at least as good as conventional solutions. Logical centralisation, off-the-shelf computing platforms, and increased system complexity represent new dependability challenges relative to the state of the art. The core function of the network, with respect to failure and service management, is orchestration. The failure and misoperation of the NFV Orchestrator (NFVO) will have huge network-wide consequences. At the same time, NFVO is vulnerable to overload and design faults.Thus, the objective of this paper is to give a tutorial on the dependability challenges of the NFVO, and to give insight into the required future research. This paper provides necessary background information, reviews the available literature, outlines the proposed solutions, and identifies some design and research problems that must be addressed.