Let me tell you about some shit.
A Beginner's Guide to Apiology by VictoryCandescence - This has been making the rounds, so it's not exactly an exciting new find. But it's great and worth a look. Be warned: this is very sweet, but also sad. It's an au where Sherlock and John meet as old men in Sussex. (There is character death.)
Read Our Futures in the Rising Steam by xzombiexkittenx - This fic was recced by someone on the chat this week (I'm sorry I forgot who- I tend to lose track of who said what in a chat environment) and it is fucking amazeballs. It is basically a casefic with some sex/relationship bits nailed on, which is the best kind of Sherlock fic IMO. It's incredibly well-written and the characterization is absolutely great. It's post-Return, Sherlock and John are still kind of hashing stuff out in a very British, manly, oh-god-let's-not-talk-about-feelings kind of way, and someone is kidnapping and vivisecting men who bear a startling resemblance to John. Lestrade is worried and loyal to his own detriment, Mycroft is caring and protective but also a massive dick, John is bamfy as hell, Donovan wins at policing, and Sherlock is the dumbest motherfucker of a genius. So it's pretty much perfect.
Ok. I try to recommend mostly new stuff people might have missed, or old stuff that's fallen out of fandom discussions and post-s2 fans might not know about. I also try not to do repeat recommendations of authors or recommendations of stuff everyone on earth has read, just to spread the love. Now I'm going to break all these rules, and make some recs in what may become a continuing series called Shit You Should Be Reading If You're Not Already (catchy!). This also technically still falls under What's On My Kindle This Week, because it totally is unless I download a new chapter and forget to sync my Kindle before I leave the house, like I did this morning.
These are all WIPs. I know a lot of people avoid those, but there's something magical and addictive about reading a story bit by bit as it unfolds.
Quintessential by thisprettywren - It's hard to explain the premise of this story without ruining the fun you get from reading Wren's incredible world-building. It's an AU, it's awesome, and there's no triggers that I can think of.
Cooperative Principle by bendingsignpost - In this au, John gets a job teaching at Barts and doesn't become Sherlock's flatmate. Instead, Sherlock seduces him and they have sex an average of five times per chapter. Also there's some deliciously-written angst, but I'm not going to lie, I'm enjoying extremely sexually forward Sherlock more than the angst. Also: desksex.
Making It Better by sideris - I've recced sideris before- specifically
Working It Out, the first chapter of which is one of my favorite things. This is their Return fic. I am excite. :D (Sideris historically has been slow to update WIPs, but updates are extremely meaty when they come.)
(Incidentally, if you were waiting for Castiron's Not Yet Dead to be complete before starting it, wait no longer. It's done.)