<p>Network services are provided through Virtualized Network Functions (VNFs), such as firewall, intrusion detection, and load balancer, arranged in a chain known as a Service Function Chain (SFC). SFC placement refers to the selection of Virtualized Network Functions (VNFs) in a predetermined order, while SFC routing involves determining the paths or links through which the data flow is forwarded from one VNF (source) to the next (destination). The combined optimization of both SFC placement and routing is commonly referred to as SFC mapping. In large-scale networks, network conditions can change rapidly, necessitating dynamic solutions for SFC mapping that can adapt to the uncertainties inherent in dynamic networks in real-time. This paper provides an insightful overview of dynamic Service Function Chain (SFC) mapping within the framework of network function virtualization infrastructure (NFVI), focusing on the optimization of SFC placement and routing to minimize latency. It highlights the challenges in identifying appropriate Virtualized Network Functions (VNFs) and constructing optimal data traffic routes. While existing literature extensively covers joint solutions for SFC mapping, there is a noticeable research gap concerning dynamic SFC mapping aimed at latency minimization. The review encompasses background information, taxonomy, and challenges associated with SFC mapping, analyzing strategies ranging from traditional methods to deep learning and swarm intelligence. A comprehensive analysis of existing works is presented, considering various parameters such as performance metrics, datasets, and optimization complexity. Additionally, the paper outlines open research issues and future directions, aiming to spur further advancements in latency-aware dynamic SFC mapping.</p>