Someone recently asked me why Jesus' family was white in a picture I posted on Facebook. Well, because that's how the artist chose to paint them. I was touched by the picture, showing a tender Joseph holding an infant Jesus while Mary slept. I like thinking of Joseph as a loving, gentle father figure. I wasn't terribly concerned about the historical accuracy. But the question made me think, so I've been doing some research. I will not include any links in this post; please use whatever research tools you like and find the information from sources you trust.
Jesus was born in the land on the southeast side of the Mediterranean Sea. The Bible gives us only one reference to what He looked like; Isaiah said He had no beauty or majesty in His appearance. I believe that means He was fairly ordinary looking, not someone who would stand out in a crowd of people in His time and place. The area was occupied by the Roman Empire, which is the whole reason they went to be taxed and ended up in a stable. I'm certain that there were some children born of Roman and Jewish parentage; that's the nature of conquest. There were some European genes in the pool by the time Jesus was born. There were probably some people with lighter skin than others as a result, but it seems likely that most people had olive skin in that time and place.
We know Jesus was a respected teacher, so He probably lived Jewish law. His beard was probably long and untrimmed, and the hair on His temples was probably long, while the rest of His hair was probably kept short, according to guidelines in the Old Testament. If He didn't stand out much, He wouldn't have stood out in manner of grooming, either.
So, if it's probable that Jesus was olive skinned with an untrimmed beard and short hair, why do so many pictures of Him depict a light skinned man with long hair and a neatly trimmed beard? The easy answer is, of course, we don't know, but maybe I can make some guesses.
There is a commandment in the Bible that we should not make graven images. During His life and immediately after His death, He was represented in pictures with a fish or other symbol, not with a likeness. No one who knew Jesus in life drew Him for us. The early followers of Christ would have been hesitant to give us an exact likeness.
Very early pictures that may be of Jesus were not captioned or labeled, so we can only guess at who the artist drew. The earliest picture with the iconic neat beard, long hair, and halo that we recognize as Jesus is from the early part of the third century, around 235 AD. The artist had never seen Jesus, and probably chose to draw Him as someone like the artist. From that time, there is a long and venerable tradition in religious Christian art to depict Jesus like this. Following in the footsteps of the great masters of the Renaissance, who followed the artists before them, modern artists still use the iconic and almost universally recognized (at least among Christians) look to depict Jesus.
My own religious tradition, The Church of Jesus Christ of Latter-Day Saints, otherwise known as the Mormons, has additional scripture that we believe. Part of the story is that a modern man, Joseph Smith, saw the resurrected Jesus. Joseph says He defied all description, and gives us no indication of what He looked like. Mormon artists, therefor, continue to use the traditional look of Jesus.
Partly, the look has held on for so many years because it is so recognizable. When you see a picture of Jesus, you know almost immediately who it is. Small children who are regular church goers of almost any Christian church will recognize Jesus in a painting they've never seen before because of His resemblance to all the other paintings of Jesus. Artists want their viewers to understand the painting, and know who is depicted.
I suspect that, with recent debate over what Jesus may have looked like, we will begin to see that iconic look evolve. We may see some pictures with a more olive-complected Jesus. We may see a longer beard or shorter hair. I also suspect that the traditional view will also continue for a long time. It's held on for 1800 years, it's not likely to go away in the blink of an eye.
Regardless of what Jesus looked like when He lived, or what He looks like now, I believe He is the savior of the world. He lived and died so that we can live again. He was the literal Son of God, genetically and spiritually. He is the rock on which I rest, comfort when I need comfort, hope for salvation and eternal life. It doesn't matter what He looks like. What matters is that He lives.