At the 2017 WWDC Apple made the vague statement that High Sierra would be the “last version of macOS to run 32-bit apps without compromise”. This doesn’t implicitly state that macOS 10.14 won’t run 32-bit apps, but it could be interrupted that way. It is also possible that macOS 10.14 will have some sort of limited 32-bit emulation, or just that the 32-bit Carbon framework will no longer get security updates.
This topic resurfaced recently, when Apple included a new 32-bit warning feature with the macOS 10.13.4 update. Now whenever you launch a 32-bit app, a message is displayed saying that “[App name] is not optimized for your Mac. This app needs to be updated by its developer to improve compatibility.”
A lot of Mac users are still running older 32-bit apps Including Microsoft Office 2011 and older versions of Adobe apps (InDesign CS 6, Illustrator CS5, Acrobat Pro X). QuickTime 7 and Quicken 2007 are also a 32-bit app. Now is the time to upgrade or transition to alternative 64-bit apps.
To run a report on a Mac to see how many 32-bit apps are installed, click the Apple and select About this Mac, then press the System Report button. Next click on Applications along the left (under the Software section), and wait for the results. In the list of applications displayed, check the “64-Bit (Intel) tab” to the far right. Anything listed as “No” is 32-bit.
UPDATE: Apple clarified this at the 2018 WWDC… Mac OS 10.14 Mojave will be the last macOS release to support 32-bit,