Painting is a very well known part of art and is also a very complex and modern style of art that has changed over many many years. The world went from da Vinci's painting in the 16th century, to Picasso's Cubism and Kandinsky's abstract art in the 20th century. Painting is quite a significant part of world history and the cultures that dominated the world up to today. From the Renaissance to Contemporary art, painting has always been important to societies, even ancient civilizations.
Painting did exist in the Roman Empire. The Roman Empire was quite an advanced civilization at the time it existed, so their arts and crafts were not all that primitive. The Romans mostly used plaster to paint and decorate the walls and surfaces in buildings (including religious ones) and on just many wooden surfaces in general. Their style and culture of painting was taken and used from the Ancient Greeks, Etruscans, and Egyptians. Many frescoes (mural paintings placed on lime plaster) have been physically found in the land around the Bay of Naples known as Campania. These works of art were executed in the common themes of religious subjects, still life, animal and human events, and topics based on Roman mythology with materials like plaster and wooden surfaces to paint on, using animal glue, gum, wax, and ground pigments.
There are numerous amount of paintings from the Catacombs of Rome, beginning in the third century AD and ending around 400, showing the later prolongation of the domestic decorative tradition in a version modified for use in burial chambers, in what was quite a modest social environment than the biggest houses in Pompeii. Painted plastered murals have also largely survived from places like Pompeii and Rome.
From Roman Egypt there are a large number of what are known as Fayum mummy portraits, bust portraits on wood added to the outside of mummies by a Romanized middle class; despite their very distinct local character they are probably broadly representative of Roman style in painted portraits, which are otherwise entirely lost.