The proliferation of emergent network applications (e.g., telesurgery, metaverse) is increasing the difficulty of managing modern communication networks. These applications entail stringent network requirements (e.g., ultra-low deterministic latency), which hinders network operators in managing their resources efficiently. In this article, we introduce the network digital twin (NDT), a renovated concept of classical network modeling tools whose goal is to build accurate data-driven network models that can operate in real time. We describe the general architecture of the NDT and argue that modern machine learning (ML) technologies enable building some of its core components. Then we present a case study that leverages an ML-based NDT for network performance evaluation and apply it to routing optimization in a QoS-aware use case. Lastly, we describe some key open challenges and research opportunities yet to be explored to achieve effective deployment of NDTs in real-world networks.