St. Luke (San Luca) is the patron saint of artists because supposedly he was a painter himself. Legend has it that he painted a portrait of Mary from life, with her actually sitting there, making it the equivalent of a photograph, I guess. Some versions of the legend say that he did the painting on a wooden table top that Joseph and Jesus had made. The story goes that Mary infused the painting with her blessings and grace, turning it into a miracle-working icon that would carry her power across the centuries.
Now I’m not sure if Luke did one painting of her or many, but there are churches all over the globe that claim to have a St. Luke painting of the Madonna, and these images have been revered for hundreds of years with lots of stories about miracles, healings, and deliverance from wars and disease. In the Middle Ages, people made pilgrimages to visit these paintings which were just as venerated as the relics of any saint.
Well, Venice has not one but three icons that were supposedly painted by St. Luke. One is the Madonna Nikopeia in the Basilica di San Marco (that’s her in the photo above), the second is the Madonna de Pace icon in San Zanipolo, and the third is the Virgin Mesopanditissa icon on the high altar of Santa Maria della Salute.
These icons were legendary before they were brought to Venice (and actually, that’s why the Venetians stole them). The Nikopeia was brought to Venice from Constantinople in 1204 as part of the spoils from the Fourth Crusade; she quickly became the most revered image in the city and she still is today. It's interesting that most of the Masses celebrated in the Basilica are held in her chapel rather than in front of the high altar where San Marco lies.
The San Zanipolo icon came from Constantinople in 1349 about one hundred and fifty years after the Nikopeia. The Salute icon was brought from a church in Crete in the late 1600’s shortly after the church was completed. Crete was a Venetian territory at that time so technically I suppose they didn’t really steal that one, but they were on the verge of losing Crete to the Turks (and Venice had a beautiful new church that needed a Madonna icon).
All three of these icons are very interesting but in truth, they don’t look like they were done by the same artist, and Mary looks quite different in each of them. Plus most historians estimate that they are closer to 1000 years old rather than the 2000 they would be if they were really painted by Luke. But it's a nice legend, and it seems that in the Middle Ages, if you had a miracle-working icon of the Madonna, you should be worried that the Venetians were going to steal it from you. :)
Other places that claim to have a St. Luke Madonna include churches in Rome, Bologna, Germany, Cyprus, Jerusalem, Egypt, and India. There’s also one in the Metropolitan Museum of Art in New York. The most famous is probably the Black Madonna of Częstochowa in Poland. The only one of the Venetian icons that is a Black Madonna is the one in the Salute (photo below isn't great since I didn't use a flash but you can kinda tell what she looks like).