The paper that is supposed to define the "waterfall methodology" is Winston Royce's "Managing the Development of Large Software Systems". Interestingly, the word "waterfall" does not appear in this paper. Neither does it say that you must proceed step-by-step, never looking back. In fact, it says the exact opposite of that and makes it clear that you need to go back to earlier steps when problems are identified. So why do so many people think Royce was advocating "waterfall" development? I believe that there are two reasons. First is that people only read as far as the second diagram that lays out the steps in software development and can indeed be read as a waterfall. Second, the paper was used as a straw man by the agile evangelists who needed something with which to beat existing ideas. If people actually read the paper they would find that there is nothing in it that is incompatible with agile (or Agile, if you prefer). It really is required reading. As is another classic paper, Parnas and Clements "A Rational Design Process, How and Why to Fake It".