The finest and most fascinating of the emperor Trajan's monuments is without a doubt Trajan's column, erected between the Greek and Latin libraries in front of the Basilica Ulpia in the Forum of Trajan. The column itself is more than 3m in diameter and rises to a height of 38m (100 Roman feet), and was constructed in 110 AD of 17 drums of marble from the Aegean island of Paros. Ascending in a spiral around the column is a continuous frieze more than 200m long, depicting in 23 turns of carved relief Trajan's military campaign against the Dacians. Contained within the frieze are around 2500 figures in 155 not-always-easily-distinguishable scenes; the frieze is separated from itself by a rough-cut band of varying thickness of the sort that, in Roman sculpture, typically represents earth. The column was originally topped with a statue of Trajan, which has since been replaced by a statue of St. Peter.
While this sort free-standing, decorated column seems to have been an entirely new form of expression (loosely based, perhaps, on Egyptian obelisks), much about the execution of the reliefs is clearly Greek in descent. The figures are typically well-proportioned, although their heads are slightly larger in relation to their bodies than Late Classical Greek works. The exception to this is the depiction of slain Romans and barbarians - their corpses are subtly out of proportion, distorted to emphasize their twisted, crumpled nature. In contrast to the earlier-style head-body proportions, this distortion mirrors much later Greek trends, first seen in some works at Pergamum. The figures on the column are often clad in some form of drapery (the barbarians' loose-fitting clothes, or Romans wearing cloaks over their armor) and when this is the case, the drapery looks very classically Greek - swirling in backdrop to the action and outlining the forms of the figures. However, the Roman artists stopped short of the Greek florid style, either in keeping with the earlier Classical proportions, or perhaps feeling that such ornamentation was not fitting to a monument to a down-to-earth Iberian soldier like Trajan.
The major theme of the column is the typically Greek triumph of civilization over barbarism, but the differentiation of civilization and barbarism is done in a very Roman fashion - with a specific, propagandistic aim in mind. The Romans are depicted as living embodiments of the Roman virtues of reason, industriousness, and discipline. The Roman soldiers on the frieze are constantly engaged in the actions that the Romans felt made them great and thus fated to overcome the forces of barbarism and chaos. The soldiers display their ratio and disciplina by fighting in organized formations, clad in standardized armor and armed with similar weapons. They are constantly exhibiting the Roman predilection for labor - when they are not fighting, they are building walls, bridges, or fortified camps. Furthermore, Trajan and the other Romans display virtus in their orderly treatment of prisoners and their clementia when accepting surrender. The Dacians are depicted as sympathetic and worthy adversaries, but sadly lacking in Roman virtues - they fight in wild mobs and build no walls or bridges; they treat their Roman prisoners with barbaric cruelty. Thus, the battle of civilization and barbarity is firmly cast in terms of a battle between Roman virtues and a lack thereof, and the inevitable victory is that of the Romans as ideals of virtue and industriousness.
Thus, while the techniques and proportions used to depict the forms of the figures is classically Greek, the manner in which the figures are portrayed is new and unique. Figures on the column are shown neither as idealized human archetypes nor as entirely accurate, true-to-life portraits, but rather as individuals possessed of an enhanced humanity. That is, they no longer are shown as ideal humans or real humans, but rather human ideals. This is well illustrated by the scene in which Trajan and his general Sura address the Roman troops. Trajan is identifiable by his features, but those features and his bearing are enhanced in order to portray Trajan as the perfect statesman and leader - obviously, a role the Romans wanted their emperor to fill. Likewise, in another scene, Trajan charges into battle with his arm raised as if to hurl forth thunderbolts in the manner of Jupiter. Here, Trajan is portrayed as the embodiment of the perfect warrior emperor, whose greatest function is to appear terrible to the Empire's enemies. Such portrayal of individuals fitting into perfected roles is not restricted to Trajan alone, either. Sura is depicted as an identifiable character who also happens to exude loyalty, inspiration, and battle-readiness, and each and every Roman soldier appears both as a man and as a living cog in the great machine of Roman civilization.
Even the Dacians are cast to fit into the slot the Romans felt they should occupy - the worthy adversary who nevertheless is doomed to defeat by a barbarous nature and lack of "Romanity." The artists who crafted the column portrayed the Dacians in a very sympathetic manner - the depiction of the Dacians fleeing their villages and enduring hardships is perhaps the kindest portrayal of an enemy to be found in the ancient world. This is a mark of the Roman mindset in the time of the Good Emperors - confident enough to be magnanimous and generous to their enemies, certain of their place - and that of their enemies - in the great order of the world.
Trajan's column is a work both of monumental greatness (Constantine is said to have sulked for three days after seeing Trajan's forum and column, for none of his own works could surpass it) and a work that demonstrates the evolution of the Romans' Greek artistic heritage. The Romans used Greek techniques and proportions to portray their characters and yet introduced their own enhancements - figures had grooves around them to enhance their relief and background details were sunken into the surface to give a greater feeling of depth. The Romans used Greek themes - the battle of the civilized and the barbaric - in new ways to express their own world views. Finally, the Romans moved away from both the Greek humanist ideal and their own earlier realism to portray people as both individuals and embodiments of idealized virtues.
I used information from Ranuccio Bandinelli's Rome, the Center of Power: 500BC - 200AD, Niels Hannestad's Roman Art and Imperial Policy, John Pedley's Greek Art and Archaeology, and John Wickstrom's lectures on "Late Antiquity and the Early Middle Ages" to prepare the report that I condensed into this writeup. Check out evilrooster's excellent writeup on the Forum of Trajan for more info on the column's environs.