over voltage (beyond reasonable tolerances) has a tendency to let the smoke out of components directly.

under voltage can do lots of things. Browning out with partial functionality can cause lots of problems. Some devices will pull about the same watts regardless of input voltage, so lower voltage means more current, and significant under voltage may require much higher than rated current and can damage connectors, leading to thermal runaway (loosened connector has more resistance -> more current -> more heat -> connector loosens). Brown outs during control sequences can lead to controlled loads running for longer than intended and over current situations too.