The Mediterranean race of which the Greeks and ancient Greeks are a part is one of the sub-races into which the Caucasian race was categorized by most anthropologists in the late nineteenth to mid-twentieth centuries. It is characterized by medium to tall stature, long or moderate skull, a narrow and often slightly aquiline nose, prevalence of dark hair and eyes, and a rosy pink to dark brown skin tone; olive complexion being especially common.

And yet, whenever we see 'ancient Greeks' in movies or series, they tend to be... well... more along the lines of 'rosy pink' than 'dark brown'. Actually, usually the bad guys tend to have slightly darker skin (sometimes rightfully so because of race, other times not so much). There is a name for this, whitewashing, and it happens with every single ethnic group--from Native American to Asian, to African--when portrayed on-screen. Recently Rebecca Pahle over at Pajiba addressed the issue of whitewashing as a reaction to a string of very white actors chosen in roles which should have been filled by People of Color (POC's).

"It fits in with the worldview of the average moviegoer that whitewashing wouldn’t be a new phenomenon—Mickey Rooney playing the Japanese Mr. Yunioshi in Breakfast at Tiffany’s is atrocious, but it also makes sense in a weird way, because that movie was made over 50 years ago, and (we tell ourselves) olden times were racist as fuck. We’re in the 21st century now. We’ve evolved.
Except, as this year has been an exercise in displaying, we really haven’t, as least not as much as some people might like to think. And so, in this enlightened age, whitewashing continues to be a thing. Exodus whitewashed African characters Moses and Rameses by casting white actors Christian Bale and Joel Edgerton. (With some uncomfortable eau de brownface on Edgerton. “But it’s sunny out, and he’s tan!” No. Cut that shit out.) Pan whitewashed Tiger Lily by making the character white and casting actress Rooney Mara. Star Trek Into Darkness whitewashed Khan. The Last Airbender whitewashed the good guys and let the bad guys be. The Lone Ranger. 21. The Prince of Persia. It just. Keeps. Happening.
There’s this weird disconnect, where the people responsible for these movies don’t seem to get that casting a white actor as a character of color, in a world where non-white actors, characters, people in general are constantly shoved aside, is a thing you Should Not Do."

Rebecca Pahle goes on to list a few of the most commonly used excuses by actors, directors and producers  about why whitewashing is actually not a problem at all. Some of the gems include:

“Believe me, I would have LOVED to cast Asians in the lead roles, but the truth is, we didn’t have access to any bankable Asian-American actors that we wanted… If I had known how upset the Asian-American community would be about this, I would have picked a different story to film.”
--Dana Brunetti, producer, 21

“Persians were very light skinned… The Turks kind of changed everything. But back in the 6th century, a lot of them were blond and blue-eyed.”
--Jerry Bruckheimer, producer, Prince of Persia: The Sands of Time

"Egypt was - as it is now - a confluence of cultures, as a result of being a crossroads geographically between Africa, the Middle East and Europe. We cast major actors from different ethnicities to reflect this diversity of culture, from Iranians to Spaniards to Arabs. There are many different theories about the ethnicity of the Egyptian people, and we had a lot of discussions about how to best represent the culture.”
--Ridley Scott, Exodus

“It would absolutely be a wonderful day of celebration if, within a few decades, we have another Moses and he’s a North African or Middle Eastern actor — what a wonderful thing…I think that people, rather than pointing fingers, should ask themselves, are they being supportive of North African and Middle Eastern filmmakers and actors? … The change will come from independent filmmaking, but audiences have to be there. Because once that happens, financiers of bigger and bigger budget films will say, ‘We can actually do business here.’"
--Christian Bale, Exodus

Look, I'm white. I'm about as white as they come--my skin is pretty much translucent. I have it easy in this world when it comes to race. I don't have to deal with discrimination based on the colour of my skin. Unlike a lot of people in this world, I don't have to worry about getting shot at by authority figures simply for breathing. I don't have to deal with not getting a job based on my skin colour. There is a good chance I will end up earning more then even black men. And yes sometimes when I watch a movie about our Gods or the culture that worshipped Them, I can forget that there is a culture being whitewashed here. In fact, I get to do that every Saturday. For POC's, it is not that easy and it is important that we keep demanding not just content featuring our Gods and ancient Hellenes, but that we demand for an accurate portrayal. Not just for our religion, but for the members of it who deserve to see themselves represented on the screen when talking about their ancestors.