The abstraction of the network node functions using virtualization methods introduced an innovative architecture called Network Function Virtualization (NFV). In NFV, every virtualization software hosts a network service recognized as a Virtual Network Function (VNF). In general, the network provider creates a Service Function Chain (SFC) for every sequence of multiple requested VNFs by the customers. Although NFV allows for a more flexible and economical approach, it is more prone to error and failure. Therefore, providing reliable provisioning for VNF chaining is one of the key issues in NFV. In this paper, we present a systematic literature review to study the pioneer research efforts that provide reliable provisioning for VNF chaining by guaranteeing the availability of the service and resource optimization. Our review is the result of the analysis of 21 screened papers. This paper presents the result of our analysis, including different aspects of a reliable provisioning algorithm, various adopted techniques for reliable provisioning, and the superiority and drawbacks of each algorithm based on the proposed criteria for the evaluation of the provisioning algorithms.