If you read up on the history of woodcuts, it doesn’t seem that there is much agreement on how early they came to be. Some say they began in Egypt and China. I even read one account that takes them back to the 2nd century A.D. in China. But, the fact is – they go back a loooooooooooooong way. It’s an ancient art form.
We do know woodcut methods reached Europe in the 1400’s. They became popular to use in book illustration, but not as art prints until much later.
Japan has a long history with woodcuts and they are famous for their unique techniques and style. They would print in one or two colors and often would paint colors onto the print after printing.