With the introduction of 5G and beyond networks, increasing intelligence and automation levels are being employed in managing and orchestrating virtualized networks. Through Machine Learning (ML) models, Network Service Providers (NSPs) can forecast and predict their networks' future state and proactively react to any potential fault, performance degradation, or change in demand stemming from the dynamic nature of the network environment. As such, ML models will become a critical component in the NSP decision-making process. However, model drift poses significant challenges and can severely degrade an ML model's performance, rendering it inaccurate and ineffective. This article discusses the various types of model drift and the dangers they pose to ML models deployed in dynamic networks. Additionally, the challenges surrounding the implementation of drift detection and mitigation schemes in resource-constrained networks are outlined. This work discusses three innovation areas to address model drift in dynamic networks, including network drift characteristic understanding, preventative ML model maintenance, and drift-resistant ML architectures. Finally, a novel drift detection and adaptation framework for dynamic networks and an illustrative 5G case study of model drift are presented.