I have a camera which outputs uncompressed HDMI. I understand that I can buy an external recorder (e.g., Atomos) to record the video, but is it possible to use an ordinary laptop (or desktop) computer instead?
Blackmagic Design's Decklink cards are a starting place for desktop computers: https://www.blackmagicdesign.com/products/decklink
For laptops there's both Intensity: https://www.blackmagicdesign.com/products/intensity
And UltraStudio: https://www.blackmagicdesign.com/products/ultrastudiousb3
Other companies also make such products (and even Blackmagic Design offer yet more options), but the above provides a range of answers to your question.
In the end, I found out that you can buy a dongle (in my case an INOGENI 4K USB) that will connect the camera to the computer via USB (amazingly, USB 3 is fast enough) or, in the case of BlackMagic Mini Recorder (which does 1080p only), thunderbolt.
The next challenge is, of course, to encode 4K fast enough on a laptop.