VIA Cyrix III/VIA C3
The VIA Cyrix III (later called the VIA C3) is a Socket 370 compatible processor designed by the Centaur team that built the various WinChip CPUs. It is not competitive with Intel Celeron unless run at a much higher relative clock speed. The Cyrix IIIs and C3s did however consume very little power compared to other offerings available for Socket 370.
Several core revisions were made and figuring out what exact CPU one has in hand is a task in itself. The most noticeable variant is the newest core revision, known as Nehemiah, which was the only variant which had it's FPU run at full speed instead of the half speed all the previous C3s had their FPU run at. A good indication to visually identify which core revision one might have in hand is to look for the voltage the CPU is designated to be run at (usually printed onto the CPU itself).
VIA had a list of compatible motherboards on their website, though it doesn't list which cores are compatible with what motherboard.
As the page of C3 compatible motherboards was taken down, the list was uploaded here