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This article reviews the resulting control challenges and modeling fallacies, at both the device and system level, and focuses on novel aspects or classical concepts that need to be revised in light of the transition to low-inertia systems. To this end, we survey the literature on modeling of low-inertia systems, review research on the control of grid-connected power converters, and discuss the frequency dynamics of low-inertia systems. Moreover, we discuss system-level services from a control perspective. 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