Gate radical wrapping the top and sides, the indexing radical. Originally 阅 pictured an inspector standing inside the gate, checking everyone who passed through. The gate frames the inspection scene that powers 'to inspect, to review, to read'.
Inside the gate, 兑 supplies the sound — duì shifted to yuè in 阅's reading. The 'exchange' meaning is dormant here; treat 兑 as the phonetic. Same series: 说 speak, 锐 sharp, 悦 happy — all share this graphic root with varying readings.