We all know that Europeans came to portray Jesus in the iconography and art as a white, dirty blonde, blue eyed man. Of course we've also seen how African Americans have interpreted Jesus as a black man, Latin Americans portraying their figures in more familiar Latino tones. Even in Asian cultures such as Korea and Japan he is portrayed as being more Asian in appearance.
The obvious explanation for this is to make the spiritual and symbolic representations of their faith more familiar and relatable to themselves.
Yet, I'm more interested in how this happened in the West, since we see the first images of "white Jesus" appearing as early as the 5th and 6th Centuries in a time when the racial and cultural mixtures of the former Western Roman and existing Byzantine Empires still had more interactions with people from the Levant whom Jesus would have looked more like.
I've considered the portrayal of Jesus as white in the Middle Ages, in the context of "proto-racial" ideas, in an earlier answer, if you're interested.