The order was arrested across France on Friday 13 October 1307 on the orders of Philip IV, and the charges were spectacular: denial of Christ, spitting on the cross, obscene kissing at reception, idol worship of a head called Baphomet, and sodomy. Large numbers of brothers confessed. The order was suppressed by Clement V at the Council of Vienne in 1312, and the last Grand Master, Jacques de Molay, was burned in 1314 after retracting his confession.
Malcolm Barber's study of the proceedings is the standard account, and its central finding concerns the confessions. They were obtained under torture, or under the threat of it, in a jurisdiction where the king had a direct financial interest in the outcome and where the pope was resident at Avignon under French pressure. The confessions are close in wording to the charges as drafted, which is what interrogation under duress against a prepared list produces. Where brothers were examined outside France, in England, in Aragon, in Cyprus, in the Papal States, and torture was applied late, reluctantly, or not at all, the confessions largely do not appear. Those who retracted did so at the cost of being burned as relapsed heretics, which is a strong indication of what the retraction cost and therefore of what it was worth.
The Chinon parchment, rediscovered in the Vatican archives and published in 2007, records that Clement absolved de Molay and other leaders of heresy in 1308, some years before suppressing the order on grounds of scandal rather than guilt. The suppression was an administrative act, not a verdict.
Historians do not treat the charges as established. The order's wealth, its exemption from local jurisdiction, and the crown's debts to it are sufficient to explain the prosecution without any of the accusations being true.
The separate question of continuity is answered more shortly. No documentary chain connects the medieval order to any later body claiming descent from it. The Templar element in eighteenth-century high-degree Freemasonry, which Peter Partner traced, was a construction of the 1730s and afterwards, built from the romance of the suppression rather than from any surviving organisation. It is a revival in the sense that the Renaissance was a revival: a later age making use of an earlier one it admired and could not consult.