I bookmarked a couple of months ago, and finally got around to reading, this article by ‘Quanta’ magazine on the story behind Freedman's proof of the 4-dimensional Poincaré conjecture — and how it was saved from being “lost”. It's quite interesting. quantamagazine.org/new-math-book-…
The statement is that any topological 4-manifold that is a homotopy sphere is, in fact, homeomorphic to a sphere. (The analogous theorem for dimension ≥5 was proved in the 1960's by Smale & others. In dimension 3 it was proved in the 2000's by Perelman.) en.wikipedia.org/wiki/Generaliz…
The gist of the story in dimension 4 is that Michael Freedman wrote a sketch of a proof in the 1980's and convinced the experts that his proof held water, but details were never fully written down beyond this basic sketch (which further contained errors).
Now a team of people made an effort to fully understand the proof (with Freedman's help), fill in the gaps, and write it in the form of a book — so it can be understood by people who don't have access to the author, and so it won't be lost in time.
The ‘Quanta’ article does a decent job at explaining to the layperson what all this mean (the statement, and the very basic ideas of the proof). But perhaps more importantly, what this says about the social concept of what constitutes an accepted “proof” in mathematics.
The following MO discussion (written before the book came out) is quite interesting to read in the latter regard. mathoverflow.net/q/87674/17064 The comment below by @andrejbauer is perspicacious as to why such attempts to fully flesh out a published “proof” are difficult to undertake. 
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