Time/utility function time constraints (or TUFs) and utility accrual (UA) scheduling optimality criteria, constitute, arguably, the most effective and broadest approach for adaptive, dynamic 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 application-or situation-specific function of that activity?s completion time. With TUF time constraints, timeliness optimality criteria can be specified in terms of accrued (e.g., summed) activity utilities. This paper overviews past and recent advances on adaptive resource management for dynamic time-critical systems using UA algorithms. Emerging challenges and new research directions are also identified.