32 Bit App Compatibility With Macos High Sierra 10.13 4
Today and tomorrow, macOS users will begin seeing notifications informing them that 32-bit apps will not be supported in a future version of macOS, Apple representatives told Ars.
Macos El Capitan
Question: Q: 32-bit app compatibility with macOS High Sierra 10.13.4 and later More Less Apple Footer This site contains user submitted content, comments and opinions and is for informational purposes only. Jan 30, 2019 Over the past couple of OS releases, Apple has made it increasingly clear that 32-bit applications are on the way out. Starting with macOS High Sierra 10.13.4, launching a 32-bit application for the first time will result in a message similar to this being displayed: macOS High Sierra 10.13.4 and later macOS Mojave 10.14.x When. Mar 06, 2018 MacOS High Sierra is the last macOS release to support 32-bit apps “without compromise” (presumably meaning without performance degradation, and with maximum compatibility), and betas of macOS 10.13.4 are now notifying users if 32-bit apps are being run. This might suggest that 32-bit Mac apps will run through a compatibility mode like. You have to do nothing, 32-bit apps continue to work on Mojave. In the future release of macOS 10.15, applications will have to be 64-bit. App developers will issue updated apps if they want their apps to work on these future releases. Or check for updates visting the applications website. 32-bit app compatibility with macOS High Sierra 10.13. Apr 11, 2018 The dialogue box can be dismissed with the ‘OK’ button or users can click ‘Learn More’ to access a newly published explainer document on 32-bit app compatibility with macOS High Sierra.

Starting at midnight April 12, 2018 in users' local time zones, they will see the following message the first time they launch an app that only supports 32-bit in macOS High Sierra 10.13.4:
This app needs to be updated by its developer to improve compatibility.
Along with that message, they'll see a 'learn more' link that takes them to an Apple support page with more information. The support page broadly explains Apple's plans to 'eventually' require all Mac software to be 64-bit. It also reiterates several statements Apple has made to developers in the past, like specifying that High Sierra will be the last version to run 32-bit apps 'without compromise:'

Apple began the transition to 64-bit hardware and software technology for Mac over a decade ago and is working with developers to transition their apps to 64-bit. At our Worldwide Developers Conference in 2017, Apple informed developers that macOS High Sierra would be the last version of macOS to run 32-bit apps without compromise.
Back in January, Apple's beta release notes for macOS 10.13.4 said that these notifications would begin going out with that version's public release, but they didn't start when that update first became available. Now, all users will be told about it the first time they open each 32-bit app.
However, the company still hasn't specified exactly when support will be ended completely. 32-bit apps will still run normally for the immediate future. The statement that High Sierra is the last version to support 32-bit 'without compromise' suggests some stop-gap measure in the next version of macOS. That update will likely come in September or October of this year, and we can probably expect further details at Apple's Worldwide Developers Conference (WWDC) in June.
Apple is making the transition to 64-bit in part because it will be easier to maintain and also because 64-bit apps are more efficient in most cases. For example, 64-bit architecture allows taking advantage of much more memory than 32-bit architecture does.
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Apple made this transition with iOS last year. In that case, it followed a similar path: Apple notified developers, then it notified users. It first stopped accepting new apps to the App Store that were not 64-bit and then later stopped launching them.
32-bit App Compatibility With Macos High Sierra 10.13.4 And Later
Apple already stopped accepting 32-bit applications to the Mac App Store. The company delivered a talk at WWDC last year to prepare developers, and it released this statement to developers to help them prepare:
The last macOS release to support 32-bit apps without compromise is macOS High Sierra. Make sure future releases of your app are 64-bit compatible by using new diagnostic tools in Xcode 9.3 beta and testing on macOS 10.13.4 beta. This version of Xcode also builds 64-bit apps by default.
How to check if your apps need updating
Apple likely won't completely disable 32-bit support for many months to come, so developers still have a while to update their apps. Still, users can already check which apps they're running on their Macs need to be updated before the transition happens. Obviously, just running the app will notify them now, but they can also get the full list through the process below.