It is unknown exactly where Trajan erected them. They are believed to have been built either on the edge of the rostrum or on the sides of the black pavement marking the underground "Tomb of Romulus". In spite of this uncertainty, they are of great historical value because the carvings show the full length of both sides of the forum at the time they were erected.
The left relief shows the destruction of tax records in the presence of the emperor, probably Hadrian in 118AD, to the tune of 900 million sesterces. The wooden tablets with the tax records are carried forth and burned in the presence of the emperor, who is standing in front of the Rostra. The practice of 'fiscal pardon' had been carried out previously under Trajan following his victory in the Dacian War in 102AD
On the right relief, depicted left to right, the buildings are: The Ficus Ruminalis and the statue of Marsyas; the Basilica Julia; the Temple of Saturn; the Temple of Vespasian and Titus; and the Rostra (only one of which are visible). A part of the relief is missing, where the Temple of Concord should have been.
On the left, again from left to right: the speakers' platform in front of the Temple of Divus Julius; the Arch of Augustus; the Temple of Castor and Pollux; the Vicus Tuscus; the Basilica Julia; the Ficus Ruminalis and the statue of Marsyas, champion of the people.