Phonological history of English close back vowels

Most dialects of modern English have two close back vowels: the near-close near-back rounded vowel /ʊ/ found in words like foot, and the close back rounded vowel /uː/ (realized as central [ʉː] in many dialects) found in words like goose. The STRUT vowel /ʌ/, which historically was back, is often central [ɐ] as well. This article discusses the history of these vowels in various dialects of English, focusing in particular on phonemic splits and mergers involving these sounds.