With the rapid expansion of distributed energy resources (DERs) within distribution networks, the need for network-aware control strategies has grown significantly to maintain network integrity. Dynamic Operating Envelopes (DOEs) offer a promising approach to addressing the challenges faced by Distribution Network Service Providers (DNSPs). However, the concept of DOEs is still emerging, and practical implementation challenges remain unexplored. Therefore, this study conducts a thorough literature review on the current state of research regarding the application of DOEs in distribution networks. Initially, we introduce DOEs and proceed with an extensive exploration of existing literature across several subdomains, including envelope positioning, allocation mechanisms, control types, envelope behaviour, fairness and equity considerations, stakeholder coordination, network visibility, uncertainties, and communication aspects. Additionally, the study summarises ongoing industry trials and pilot projects involving DOEs. Moreover, it identifies implementation challenges such as public acceptance, regulatory frameworks, technological readiness, allocation fairness, constraint prediction, and network visibility. Finally, the paper concludes by proposing future research directions for effectively implementing DOEs in distribution networks.