As 5G and Internet-of-Things (IoT) are deeply integrated into vertical industries such as autonomous driving and industrial robotics, timely status update is crucial for remote monitoring and control. In this regard, Age of Information (AoI) has been proposed to measure the freshness of status updates. However, it is just a metric changing linearly with time and irrelevant of context-awareness. We propose a context-based metric, named as Urgency of Information (UoI), to measure the nonlinear time-varying importance and the non-uniform context-dependence of the status information. This paper first establishes a theoretical framework for UoI characterization and then provides UoI-optimal status updating and user scheduling schemes in both single-terminal and multi-terminal cases. Specifically, an update-index-based scheme is proposed for a single-terminal system, where the terminal always updates and transmits when its update index is larger than a threshold. For the multi-terminal case, the UoI of the proposed scheduling scheme is proven to be upper-bounded and its decentralized implementation by Carrier Sensing Multiple Access with Collision Avoidance (CSMA/CA) is also provided. In the simulations, the proposed updating and scheduling schemes notably outperform the existing ones such as round robin and AoI-optimal schemes in terms of UoI, error-bound violation and control system stability.