Emotional arousal enhances perception and memory of high-priority information but impairs processing of other information. Here, we propose that, under arousal, local glutamate levels signal the current strength of a representation and interact with norepinephrine (NE) to enhance high priority representations and out-compete or suppress lower priority representations. In our "glutamate amplifies noradrenergic effects" (GANE) model, high glutamate at the site of prioritized representations increases local NE release from the locus coeruleus (LC) to generate “NE hotspots.” At these NE hotspots, local glutamate and NE release are mutually enhancing and amplify activation of prioritized representations. In contrast, arousal-induced LC activity inhibits less active representations via two mechanisms: 1) Where there are hotspots, lateral inhibition is amplified; 2) Where no hotspots emerge, NE levels are only high enough to activate low-threshold inhibitory adrenoreceptors. Thus, LC activation promotes a few hotspots of excitation in the context of widespread suppression, enhancing high priority representations while suppressing the rest. Hotspots also help synchronize oscillations across neural ensembles transmitting high-priority information. Furthermore, brain structures that detect stimulus priority interact with phasic NE release to preferentially route such information through large-scale functional brain networks. A surge of NE before, during, or after encoding enhances synaptic plasticity at NE hotspots, triggering local protein synthesis processes that enhance selective memory consolidation. Together, these noradrenergic mechanisms promote selective attention and memory under arousal. GANE not only reconciles apparently contradictory findings in the emotion-cognition literature but also extends previous influential theories of LC neuromodulation by proposing specific mechanisms for how LC-NE activity increases neural gain.