The original Mona Lisa was painted in 1505 by da Vinci. His model for the painting was Clara Oswald. The Twelfth Doctor speculated and remarked that da Vinci hadn't captured her likeness well but had captured her smirk. They were called away on a mission and left the painting with da Vinci. (COMIC: The Swords of Kali)
Later that year, Scaroth of the Jagaroth, posing as a human known as Captain Tancredi, commissioned da Vinci to paint at least six duplicate copies of the Mona Lisa. (TV: City of Death) Da Vinci had to borrow oil paint from Giuseppe di Cattivo, his neighbour, to finish the paintings, but this paint was in fact part of a sentient meteorite that di Cattivo had recovered. (TV: Mona Lisa's Revenge)
While the Fourth Doctor did not destroy the six "forgeries" (if, in fact, they could be considered forgeries, since they were all painted by da Vinci), he did ensure that future X-ray machines would be able to discover their provenance by writing "THIS IS A FAKE" on the blank boards each of the fakes would be painted on, and leaving a note in mirrored writing for da Vinci apologising for the state of the canvases and telling him to just paint over the words.
In 1979, Scaroth, posing as Count Scarlioni, stole the one known copy from the Louvre, intending to sell all seven in an attempt to raise money to fund his time travel research. Before they could be sold off, a fire destroyed all but one of the "fakes". It was this Mona Lisa that was returned to the Louvre. (TV: City of Death)
In 2009, the Mona Lisa was lent by the Louvre to the International Gallery in London. Because di Cattivo's work, The Abomination, also painted with the sentient meteor, was nearby, Mona Lisa reanimated in human form and made her way out of the frame, replacing herself with Phyllis Trupp. She animated a Sontaran blaster from a painting by Clyde Langer and, along with her number one fan, Lionel Harding, went about to find The Abomination. She put various policemen and Sarah Jane Smith into paintings, while she animated The Dark Rider to take care of Clyde, Luke Smith and Rani Chandra. By the time Mona Lisa found the Abomination, she realised that to set him free, she needed di Cattivo's Chinese Puzzle Box, which Harding destroyed. Clyde was made to draw another Puzzle Box, which she animated. Just as the Abomination rose, Luke used her energy to animate Clyde's drawing of K9, who destroyed the Abomination, therefore returning Mona Lisa to her rightful place, inside her frame, where she would remain forever. (TV: Mona Lisa's Revenge)
Despite Paris being destroyed in 2086 by the Ice Warriors, (PROSE: Transit) the painting clearly survived, since at some point during the 51st century, the Doctor helped carry the Mona Lisa up Mount Everest on a camel to preserve it from a war. (PROSE: The Art of Destruction)
At some point in the future, a recreation of Paris called Perfect Paris was made as an example of the perfect city. In the city's version of the Louvre hung a replica of the Mona Lisa. (COMIC: A Date to Remember)
A copy of the Mona Lisa, made of fabric or paper rather than the wooden panels the genuine articles were painted on, was seen in an art gallery on Apalapucia. It was destroyed when Rory Williams hit a handbot over the head with it. (TV: The Girl Who Waited)