The download goes to your Downloads folder. Click the downloads arrow in your browser toolbar, or open Finder and pick Downloads from the sidebar. Press Command and J in Chrome for the full list.
It arrives as MP3 and opens in QuickTime, IINA, VLC, iMovie and Final Cut Pro without any conversion step. Because it is written straight to storage rather than into an app’s private folder, anything on macOS Ventura, Sonoma and Sequoia that can open it can reach it.
Recording starts the moment you press download and runs until the Space ends or you stop it. Anything said before you started is not in the file: while a Space is live, X publishes only its last few seconds. If the host is recording it, download it again once it ends to get the whole thing.
On a Mac there is one practical consequence: the recording continues only while the browser tab is open. Locking the screen or switching apps can suspend it, so for a long stream it is worth keeping Safari, Chrome, Firefox or Arc in the foreground and the device on power. Stopping early is safe — whatever has been written is already playable.
A Space comes to about 85 MB an hour, so even a long one stays small enough to keep on a phone.
That matters more on a phone than on a computer. If you are recording something that may run for hours on mobile data, the lower renditions exist for exactly this: the file is a fraction of the size and, on a screen this size, the difference is far harder to see than the difference in your data allowance.
If Safari opens the video in a tab instead of saving it, hold Option while clicking download. Safari previews media it recognises, and Option forces it to write the file to disk instead.
If the stream itself will not load, the cause is usually the stream rather than the device. A X Space that has ended without being kept by its host is not available to anyone afterwards, and neither are private or restricted ones. Copy the link from the stream’s own page rather than from a quote or a notification, and most remaining failures clear up.
Copying links gets tedious. In the address bar of any X Space, replace x.com with downloadthisx.com and press enter: the page opens with that stream already read, ready to record.
It works in Safari, Chrome, Firefox or Arc exactly as it does anywhere else. It is the same page you are on now, reached by a shorter route.
Only public streams can be read; anything behind a login or restricted by its host is out of reach by design.
Keeping a recording for yourself is ordinary. Republishing it is not: the people speaking hold rights in what they said, and recording it to your Mac does not change who owns it.