A huge aspect of Roman art was portraiture and may have stemmed both from the Republican funerary masks, created for the dead elite and hung in their houses, and the Roman desire to be remembered.

Republican Period
Roman Republican portraiture is characterized by verism influenced by Hellenistic portraiture, and survives mainly as marble and bronze sculpture. Roman portrait busts are thought to derive in part from death masks or funerary commemorations, as elite Romans displayed ancestral images in the atrium of their home.

Portraiture in Republican Rome was a way of establishing societal legitimacy and achieving status through one’s family and background. Exploits wrought by one’s ancestors earned them and their families public approbation, and more; a pompous state funeral paid for by the state. Wax masks would be cast from the family member while they were still living, which made for hyper-realistic visual representations of the individual. These masks would be kept in the houses of male descendants in memory of the ancestors once they had passed. These masks served as a sort of family track record, and could get the descendants positions and perks.
The Patrician Torlonia bust thought to be of Cato the Elder. Bronze bust of Scipio Africanus. (c) Miguel Hermoso Cuesta AN old man with head covered, either a priest or paterfamilias, 1st c. BC. (c) shakko The Arles bust, possibly of Julius Caesar, c. 46 BC. (c) mcleclat Togatus Barberini. Bronze bust of L. Caecilius Iucundus, Pompeii. (c) Daderot
Imperial Period
With the establishment of the principate system under Augustus, the imperial family and its circle soon came to monopolize official public statuary.

Official imperial portraits were carefully designed to project specific ideas about the emperor, his family, and his authority. These sculptures were extremely useful as propaganda tools intended to support the legitimacy of the emperor’s powers and so took a step away from Republican verism and became idealised portraits.
Germanicus. (c) Waterborough Julia Flavia, daughter of Titus. (c) Wolfgang Sauber Trajan. Vibia Sabina, wife of Hadrian. Septimius Severus. Julia Domna, wife of Severus.
Frescoes
The excavations of Pompeii unearthed Roman fresco portraiture of those who lived in the city before its destruction.

2. Man wearing a laurel wreath and holding a papyrus rotulus, Pompeii.
Fayum Mummy Portraits
These are a type of naturalistic painted portrait, which covered the faces of bodies that were mummified for burial, on wooden boards attached to upper class mummies from Roman Egypt.

About 900 mummy portraits are known at present. The majority were found in the necropolis of Fayum. Due to the hot dry Egyptian climate, the paintings are frequently very well preserved, often retaining their brilliant colours seemingly unfaded by time.
Gilded portrait of a young man. Egyptian Museum, Berlin. Woman with ringlet hairstyle. Museum of Scotland. A boy, identified by inscription as Eutyches, Metropolitan Museum of Art. A woman named Isidora, c. 100-110 AD. Getty Villa. (c) Dave & Margie Hill Priest of Serapis, c. 140-160 AD. British Museum. Woman with plaited hairstyle, dating to Trajan’s reign. Walters Art Museum.
Funerary Portraits
While the Roman elite commemorated themselves with busts and statues, the lower classes, especially freedmen and soldiers, captured their likenesses on their own funerary monuments.
Tombstone of Gaius Volumnius and his wife, c. 1–50 AD. (c) Anagoria Tombstone of M. Caelius, centurion of the 18th legion, who died in the Teutoburg Forest, 9 AD. Funeral relief of a father and his children, 2nd-3rd c. AD, Palmyra. Funerary relief of Ti. Julius Vitalis, who was a butcher. Funerary relief of L. Antistius Sarculo and his wife Antistia Plutia, c. 30–10 BC. Rome. (c) Mogadir Funerary relief of Aurelius Hermia and his wife Aurelia Philematum, former slaves who married after their manumission, 80 BC, from a tomb along the Via Nomentana in Rome.
For Portraits on glass, see Roman Glass.