In China, you almost always take off your outdoor shoes and put on 拖鞋 when entering someone's home. Hosts typically provide guest slippers. Wearing outdoor shoes inside is considered rude.
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Related footwear: 凉鞋 (liáng xié, sandals), 运动鞋 (yùndòng xié, sneakers), 皮鞋 (pí xié, leather shoes), 高跟鞋 (gāogēn xié, high heels).