The process that runs today was set out by John Paul II in the apostolic constitution Divinus Perfectionis Magister of 1983, and it moves a candidate through named stages. A cause opens in the diocese where the person died, and the candidate is a Servant of God while that inquiry gathers evidence and every written word attributable to the person is examined. When the Congregation accepts that the person practised virtue to a heroic degree, or died a martyr, the pope declares them Venerable. Beatification normally follows on a miracle attributed to their intercession, and permits public veneration in a defined place or community; martyrdom dispenses with that first miracle. Canonisation, which extends veneration to the whole church, normally requires a second.
The miracle requirement is where the process does its most unusual work, because the claim examined is almost always a medical one. The Congregation refers alleged healings to a board of physicians, the Consulta Medica, whose members are asked a question that is deliberately narrower than the theological one: whether the recovery can be explained by the medicine of the day, given the diagnosis, the treatment and the course. A finding that it cannot is not a finding that God acted. That second judgement is made afterwards, by theologians and then by the pope.
The 1983 reform also changed the shape of the argument. The office of Promoter of the Faith, whose holder was popularly called the devil's advocate because his job was to attack the case, was reduced to a promoter of justice presiding over the discussion. Kenneth Woodward's reporting on the congregation in the 1980s records the complaint that followed, that removing an adversary from the procedure made causes easier to win.