In this article, we survey the main models, techniques, concepts, and results centered on the design and performance evaluation of engineered systems that rely on a utilization-dependent component (UDC) whose operation may depend on its usage history or assigned workload. Specifically, we report on research themes concentrating on the characterization of the capacity of channels and the design with performance guarantees of remote estimation and queueing systems. Causes for the dependency of a UDC on past utilization include the use of replenishable energy sources to power the transmission of information among the sub-components of a networked system, and the assistance of a human operator for servicing a queue. Our analysis unveils the similarity of the UDC models typically adopted in each of the research themes, and it reveals the differences in the objectives and technical approaches employed. We also identify new challenges and future research directions inspired by the cross-pollination among the central concepts, techniques, and problem formulations of the research themes discussed.