The runtime landscape at a glance
If you maintain something that started life as a Flash project, you have more options than a few years ago, and each one solves a different problem. This is a quick map. Check each vendor's own pages for current versions and support terms before you commit to a plan.
Browser plug-in: retired
The browser plug-in reached its announced end of life on 31 December 2020, and mainstream browsers no longer ship it. Anything that depended on a page loading a SWF in a browser needs another route.
Emulation
Ruffle is an open-source emulator written in Rust that can run many SWF files in a modern browser through WebAssembly. It is the lowest-effort option for keeping old animations and games playable, but compatibility depends on which ActionScript features a given file uses.
The AIR runtime
Adobe AIR, used for desktop and mobile apps, continues to be maintained by HARMAN. If your product is an AIR app rather than a browser embed, you may not need to change platforms at all. Your work is mostly keeping up with operating system changes, store rules and native extensions.
Open-source ports
OpenFL is a framework built on Haxe that re-implements much of the Flash display API. Many ActionScript 3 projects can be moved across with a manageable amount of rewriting, and the result compiles to HTML5, desktop and mobile targets.
Export from Animate
Adobe Animate can publish to HTML5 Canvas and other formats. This suits timeline-heavy animation and banner work, where the content is mostly drawing and tweening rather than application logic.
Not sure which fits? Read Moving a legacy SWF project to a modern runtime for a decision path.