In November, 1931, Archbishop Byrne of Dublin, Ireland opened an inquiry into the alleged claims to holiness of Matt Talbot. The Vatican began their official inquiry in 1947, and Matt was noted as "A Servant of God." In October, 1975, Pope Paul VI declared him to be "Venerable," which does not require a miracle. A physical miracle will be required to be declared, "Blessed,"
and a second miracle to be declared a "saint."
In order to learn more about the meaning of beatification, canonization, and sainthood, some resources are listed:
Vatican website, with new procedures in the rite of beatification.
Vatican website, with new procedures
New Advent Catholic encyclopedia provides a helpful discussion of beatification and canonization, beginning with its history.
http://www.newadvent.org/cathen/02364b.htm
This very readable article briefly notes the types of saints, types of virtues, titles of candidates, requirements for miracles, and the beatification and canonization processes: http://www.overcomeproblems.com/saints.htm
This article addresses those individuals who might be more likely to be canonized and does mention Matt Talbot:
http://www.stthomasirondequoit.com/SaintsAlive/id697.htm
Wikipedia provides extensive discussion and links about beatification, canonization, and sainthood. (Beware, however, that anyone can edit the content.) http://en.wikipedia.org/wiki/Canonization
Stages of Canonization in the Roman Catholic Church (Wikipedia)
Servant of God → Venerable → Blessed → Saint
An excellent book on this topic is, "Making Saints: How the Catholic Church determines who becomes a saint, who doesn't, and why" (1990) by Kenneth Woodward. This book can be found in many USA public libraries.