The Genesis Gap and its Origin in Bible Doctrine

What has been called the "Gap Theory" was a popular and consistent explanation of the first chapter of Genesis among Christians up through the mid 1900s. With the rise of Young Earth Creationism, the Gap understanding was simply pushed to the background and ridiculed as a past effort to satisfy the claims of modern evolutionary science. In effect the new teachers buried this doctrine with the debris of Noah's flood deposits. What does the Bible really teach about a Gap? Does a Gap have any basis in Bible Doctrine?