Reading Recovery (RR) was developed in New Zealand in the early 1980s to provide 30 minutes of daily individualised literacy instruction over 20 weeks for students struggling with learning to read after one year of formal schooling. Considerable research has been undertaken on the RR programme. While results indicate short-term success for some students, each year 15-30% of students do not successfully complete the programme and are therefore 'unrecovered'. Research on the characteristics of these unrecovered students is sparse. This review examines findings on the characteristics of unrecovered students. These RR students typically have limited phonemic awareness and phonemically based decoding skills, and lower scores on RR screening measures on entry to RR than 'recovered' students. In New Zealand, unrecovered students tend to be enrolled in schools serving lower socio-economic neighbourhoods, and tend to be from Maori or Pasifika (Polynesian Pacific Island heritage) backgrounds. These students typically receive more RR lessons than recovered students. We conclude that RR does not tailor instruction to meet the needs of individual students, as claimed. The RR instructional model, developed in the 1970s, fails to recognise the importance of explicit, systematic instruction in phonemic awareness and the use of letter-sound relations. Such instruction is essential for most students who struggle with literacy learning during their early years of schooling and especially important for students who experience the most difficulty with learning to read. Suggestions are presented for strengthening the RR programme and for reducing the number of unrecovered students.