Cyrix was bought by Via (via National Semiconductor) and rolled into their Isaiah architecture along with Centaur's architecture. That was then used in Nano[1]. It is now being used in Chinese co-developed and fabbed x86 options[2].
The rest of their technology was bought by AMD and used in it's MediaGX/Geode chips[3].
The rest of their technology was bought by AMD and used in it's MediaGX/Geode chips[3].
1 - https://en.wikipedia.org/wiki/VIA_Nano
2 - https://en.wikipedia.org/wiki/Zhaoxin
3 - https://en.wikipedia.org/wiki/Geode_(processor)#AMD_Geode