River Teviot, tributary of the River Tweed, southern Scotland. Its valley, Teviotdale, constitutes a large part of the historic county of Roxburghshire. The river, rich in trout, flows northeast past Hawick to join the Tweed at Kelso. The alluvial haughs and gravel terraces of the valley floor are improved farmland, but much of the basin consists of steep, rounded hills used for rough sheep grazing.