I still remember bumping into this in Trope Bingo a few years ago and going huh, new word, what does Epistolary mean? And now it is one of my favorite things, although I wouldn't call it a trope? It's more like a narrative device: a story told/inferred through written communication like letters, and so associated tropes are often long distance relationships and/or body swap. The "documents" often add to the sense of realism/worldbuilding, and so much can be inferred about how two people feel about each other via the tone of their communications as well.
I love the whole idea of falling in love with someone when all you've ever done is talk to them through letters. Stephen King said that writing is basically telepathy, and it's true: it's a transmission of thoughts via words on a page and therefore all of the physical stuff that comes with reality (class differences, gender roles etc.) doesn't matter. The other person only exists in your mind-- until their "voice" forges a more tangible connection because it's sunk roots into your emotions. There's also the associated romantic thrill of carrying around letters like warm little totems and re-reading them when you want to blow on the coals again. Knowing their handwriting; their turns of phrase, that you've made them smile a thousand miles away is its own form of intimacy. I also find it easy to read- I'm not a huge fan of huge, prosey paragraphs and letters are basically written dialogue that you are "eavesdropping" on.
Of course, in this modern age we aren't bound to letters, newspaper clippings and diary entries, and epistolary works can be done with emails, text messages and all sorts of social media as well. Some helpful people on AO3 have even created workskins so your epistolary fic can look realistic! (iOS messages and Emoji) (Instagram, Twitter)
I think the first time I wanted to shriek with glee was reading Darcy's letters to Elizabeth in Austen's Pride and Prejudice way back when and most recently Amal El-Mohtar's This is How You Lose the Time War absolutely blew me away. Title is from Red/Blue's first daring exchange- I reviewed this book here, but it is enemies-to-lovers time-travelling assassin/spy epistolary sci fi, and poetic and potent and absolutely wonderful. Their creative letters are just delicious. (Sometimes literally!)
Andy Weir's The Martian is also mostly epistolary (Mark Watney's video journal entries and emails) and such a joy to read because Watney is a fantastic narrator. He's honest about the odds and how he feels about them, and he explains the science (and his thoughts in conjecture) in hilarious, geeky detail with plenty of non-censored swearing. (The film is very true to the book, and also wonderful.)
Kimi no Na Wa/Your Name is a body swap film, so it also has epistolary elements (I've been translating the letters/texts from the movie- the voice actors "read aloud" some of what they write to each other in the movie, but if you think about it, the characters never actually spoke to each other except through their messages) and I also loveloveloved The Lake House, which also had the characters writing each other through time and reading the letters aloud.
Some fic recs:
10 things I hate about reunions by BryroseA (10 things I hate about you, Kat/Patrick, 17278 words) The epistolary part is texts between Bianca and Kat. Sidetrope to love in this is Sibling Meddling!
THIS IS HOW YOU SURVIVE THE COHABITATIONAL BLISS AFTER YOU WIN/LOSE THE TIME WAR by ScottLynch78 (This is How You Lose the Time War, Red/Blue, 551 words) Amal El-Mohtar was actually reccing this fic off her Goodreads page, so you know it's quality fic!
at heyitsspiderman by meggannn (Into the Spiderverse, Team Spidey, 27000 words) This fic is mainly the delightful Spider group chat, complete with embedded soundcloud music, although other epistolary parts are Post-its on a wall that may make you tear up. It's funny and exciting and touching, in the exact flavour of the film. A+ characterization
Revisions to a 'Dear Writer' letter, Yuletide 2035 by Lanna Michaels (The Martian, 1313 words) This fic is hilarious, heart wrenching and thoroughly delightful. Imagine you requested NASA RPF for Yuletide the year Watney "died" and then ended up stranded on Mars.
Tidings of comfort and potatoes by filigree (The Martian, Mark Watney/Mindy Park,16837 words- incomplete) This was the first epistolary fic I straight up adored, and I've recced this before and I'll do it again. Love even the banality of the auto-reply emails in this because they make it so much more real.
flowers from strangers by Odyle (Greek Mythology, Eros/Psyche, 6651 words) The same tale, as a modern AU. I had no idea I needed it until I read this.
And of course, I have included epistolary in some of my own fics:
To Temper Steel (Game of Thrones, Arya/Gendry, 14766 words) Post canon fix-it, the epilogue chapter is done in epistolary format, mostly letters but also a lineage listing.
Newton's First Law (The Martian, Beck/Johanssen, 16941 words) Canon compliant fic exploring how they got together and how the crew fared in the part time-skipped over in the film and book. Epistolary is in the 3rd chapter- emails from NASA and their families and friends and back.
Bound (Game of Thrones/A Song of Ice and Fire, Arya/Gendry, 34488 words) Body swap fic, so they talk through letters throughout the fic.
Revelations (Nolanverse Batman, Selina/Bruce, 12000 words, WIP) Coda fic, filling in the gaps in that final montage we get in TDKR. Epistolary is in the 3rd chapter, texts between Selina and Bruce and Selina and Jen from TDKR.
I would love more recs (both fic and new canons!), so HMU in the comments if you have any!