This position paper makes the case that timeutility functions or TUFs and utility accrual optimization criteria constitutes, arguably, the most effective and broadest approach for adaptive, time-critical resource management. A TUF, which is a generalization of the classical deadline constraint, specifies the utility of completing an application activity as an applicationsituation-specific function of that activitys completion time. With TUF time constraints, timeliness optimization criteria can be specified in terms of accrued activity utilities. Such utility accrual or UAcriteria facilitate design of resource management algorithms that are adaptive in the sense that they allocate resources in a mission-oriented way i.e., in the best interests of the applications mission. Further, they gracefully degrade timeliness performance during overloads and gracefully improve performance otherwise. Such timeliness adaptivity is not possible with traditional real-time resource management techniques. We overview past and recent UA algorithms that illustrate this. We also identify emerging challenges.