A preprint “is a version of a scholarly or scientific paper that precedes publication in a peer-reviewed scholarly or scientific journal” (Wikipedia). Examples of lists of preprint servers are available here and here. A list of disciplinary eprint repositories can be found here.
A blog post, The rising tide of preprint servers, provides a brief description of evidence that preprint servers such as bioRXiv are gaining wider acceptance. One example is provided by the statement (March 24, 2017) by Andy Collings, the Executive Editor of the Open Access journal eLife, that Authors can now submit a preprint to bioRxiv while submitting to eLife.
A short history of preprint servers is available in an article (September 29, 2017) by Jocelyn Kaiser in Science magazine, entitled: Are preprints the future of biology? A survival guide for scientists. It’s mentioned in this article that: “In the 1960s, the National Institutes of Health (NIH) in Bethesda, Maryland, mailed photocopies of draft manuscripts to groups of biologists…”. The project was short-lived. I’ve provided a few details about these Information Exchange Groups (IEGs), and have suggested that they can be regarded as Predecessors of preprint servers.
My own opinion is that Overlay Journals have a rosy future. For more about Overlay Journals, see: Open journals that piggyback on arXiv gather momentum. I’m not aware of any Overlay Journals in Biology or Medicine, but predict that there will be some (eventually).
Be openly accessible or be obscure 