I'm sure this is not news to many; ancient Hellenic sculptures were not left bare and white: they were painted in vibrant hues of blue, red, and yellow, often embellished with gold, and adorned with jewelry. The ancient Hellas Hollywood tries so valiantly to feed us is, in fact, very dull and dreary. Depending on the translation Euripides' play 'Helen [of Troy]' even reflects this:

"My life and fortunes are a monstrosity, partly because of Hera, partly because of my beauty. If only I could shed my beauty and assume an uglier aspect, the way you would wipe color off a statue."

The idea of white marble dates back to the early 16th century, when the Renaissance began excavating statues that had been buried in the earth for centuries. Color traces still visible to the naked eye, deep in the folds of draped clothing, went unnoticed. Following what they believed to be the Greek and Roman example, Italian sculptors conceived their creations as uncolored, and suddenly all statues ended up plain white marble.

A couple of years ago the Vatican Museum hosted an exhibition called 'The Colours of White' of some of the most famous classical statues and antiquities with reproductions painted as close to the originals as they could make them, made possible because many statues contain trace amounts of pigment from their original coats of paint.

In order to identify paint and color, UV light is used. UV light makes many organic compounds fluoresce. The technique is usually used by art dealers to check if art has been touched up--since older paints have a lot of organic compounds and modern paints have relatively little--but on ancient statues, UV light makes the tiny fragments of pigment still left on the surface light up to become visible to the naked eye.

Even if you disregard colors fading and changing over time, many spots of paint can't be interpreted as specific colors. To distinguish color, scientists look at the original plant and animal-derived materials used to create the pigments of the paint. These materials are anything from crushed stones or shells to insects and plant roots. These materials do not change over time, and would still look the same today as they did thousands of years ago.

To identify these materials, the statues are flooded with infrared and X-ray spectroscopy. This technique relies on the fact that atoms are picky when it comes to what kind of incoming energy they absorb. Certain materials will only accept certain wavelengths of light; everything else they reflect. Spectroscopes send out a variety of wavelengths, and the pattern of wavelengths which are not returned are compared with materials known to be used for paint colors. Infrared helps determine organic compounds, X-rays identify rock and mineral material. Together, researchers can determine approximately what color a millennia-old statue was painted.

At the start of this identification process was German archaeologist Vinzenz Brinkmann. He has spent the past quarter century trying to identify colors and create full-scale plaster or marble copies hand-painted in the same mineral and organic pigments used by the ancients: green from malachite, blue from azurite, yellow and ocher from arsenic compounds, red from cinnabar, black from burned bone and vine.

This process, and the results, can be viewed in the video below:

Personally, I think the ancient statues look gorgeous in their reconstructed color glory. They bring life to them, and show how devoted (and/or vain) the procurers of these sculptures were: vibrant colors--or really colors of any kind--would have been incredibly expensive. I have seen people react to these painted statues with disdain, feeling the ancient Hellenes would have most likely not used such gaudy colors, but I think they would have: only the best for the Gods they worshipped, the victors of athletic competitions, and heroic soldiers.
I have been looking to paint my own small collection of statues for a while, and was going to do so yesterday when I unexpectedly ended up pulling flooring at a friend's house for the majority of the day, so if I get a chance, I will do this today and edit this post with pictures. I think reflecting the ancient Hellenic way of making statues--namely, painted, and sometimes clothed--is an important part of the modern Hellenistic mindset, and would love to hear if you agree.

EDIT: I found the time to paint both my statue of Pandora and the karyatis who resides on my altar permanently today. Here is the result, although they are not yet finished. Both still need gold and touch-ups.

Image source: Smithsonian