The good news that everyone was waiting for — the official Xposed for Lollipop/Marshmallow/Nougat (Android 7.1, v88.2) is here.
XposedInstaller_*.apk from this thread: Must be installed to manage installed modules, the framework won't work without it.
xposed*.zip from http://dl-xda.xposed.info/framework/: Must be flashed with a custom recovery (e.g. TWRP) to install the framework.
SDK21 is Android 5.0 (Lollipop), SDK22 is Android 5.1 (also Lollipop) and SDK23 is Android 6.0 (Marshmallow).
For Nougat, SDK24 is Android 7.0 and SDK25 is Android 7.1.
I only support the latest Xposed version per Android release!
xposed-uninstaller*.zip from http://dl-xda.xposed.info/framework/: Can be flashed with a custom recovery (e.g. TWRP) to uninstall the framework.
The small .asc files are GPG signatures of the .zip files. You can verify them against this(https://pgp.mit.edu/pks/lookup?op=vindex&fingerprint=on&exact=on&search=0xE82F08717235F333) key (fingerprint: 0DC8 2B3E B1C4 6D48 33B4 C434 E82F 0871 7235 F333). That's actually the master key, the files are signed with subkey 852109AA.
Known issues:
- Before Nougat: Bootloops on Samsung stock ROMs. That's due to Samsung's changes to ART. There are unofficial builds that work around this by deodexing and adjusting the ROM.
- Sony seems to have shipped some ROMs with corrupted services.odex (the embedded .dex is invalid). Those ROMs will bootloop with a "Fatal signal 6" or "No pending exception expected: java.lang.ArrayIndexOutOfBoundsException" error, which I unfortunately cannot fix (see https://github.com/rovo89/Xposed/issues/64)
- Dell ships (at least) their Venue 8 7840 with a non-standard version of ART that is somewhere between 5.1 and 6.0 which obviously isn't supported by Xposed (see https://github.com/rovo89/Xposed/issues/77)
Xposed Framework:—
http://dl-xda.xposed.info/framework/
Xposed Installer 3.1.3:—
https://forum.xda-developers.com/attachment.php?attachmentid=4318364&d=1509375742
Xposed Installer 3.1.4:—
https://forum.xda-developers.com/attachment.php?attachmentid=4319220&d=1509453299
Xposed Uninstaller:—
http://dl-xda.xposed.info/framework/uninstaller/
Discussion Thread:—
Lollipop - https://forum.xda-developers.com/xposed/official-xposed-lollipop-t3030118
Marshmallow - https://forum.xda-developers.com/xposed/discussion-xposed-marshmallow-t3249095
Nougat - https://forum.xda-developers.com/xposed/discussion-xposed-nougat-t3685687
Announcement Thread:—
https://forum.xda-developers.com/showthread.php?t=3034811
How I install this on phone? - shared by dcs18
Download the correct SDK Framework as per the API of your device.
Download the Xposed Installer (V3.1.2 — as of typing this post.)
Download the Xposed Uninstaller (20160829 — as of typing this post.)
Copy all the above 3 downloaded files to your SD Card.
Boot into Recovery (TWRP is my favorite one) to flash the Framework.
Boot into the system to install the Xposed Installer just as any other .apk.
If anything went wrong, boot back into Recovery to flash the Xposed Uninstaller.
If everything went right, download your fav. modules to install them just as any other .apk.
FYI: Must unlock boot loader?
Whether or not the bootloader should be unlocked differs from device to device and also from ROM to ROM — before flashing Xposed, would recommend performing a full Nandroid backup and manually backing-up contents of the SD Card, as well. 
For phones with locked bootloaders like my American S7, try Flashfire: https://play.google.com/store/apps/details?id=eu.chainfire.flash to flash the .zip.