Update: The Android Security team has posted the September 2015 Nexus Security Bulletin at the Android Security Google Group. These updates have been released over the air, and you should expect a notification to update when it pushes to your device. The details of exactly what was patched (with accreditation) has also been posted. Interested parties should read it here.
Google recently promised monthly security updates for currently supported Nexus phones and tablets, and today we see the results — new factory images for the Nexus 6, the Nexus 9, the Nexus 5, the 2013 Nexus 7, the Nexus 10 and the Nexus 4.
The latest version (in most cases) checks in as LMY48M, and should include the very latest behind-the-scenes patches and fixes for current and future security issues. Of course, new exploits and bugs will be discovered, and Google will bang out another round of updates.
Remember, if you're using a Nexus 6 on T-Mobile you'll want to download the special LYZ28J build, and Project Fi users should grab build LVY48E. These devices have their own version with special network enhancements for Wifi calling and cell to Wifi handoff. With Marshmallow, these should be integrated into the shipping software, but for now grab the right version to use all the features available to you. But don't worry — flashing the "wrong" version doesn't really hurt anything. Don't ask how we know this.
There's no news (yet) from any other manufacturers about when we can expect these security fixes for other phones, nor anything about when OTA updates will start rolling out for the supported devices. We'll fill you in when we find out.