I've been interested in VIA motherboards and CPUs ever since they came up with the Mini-ITX standard in the very early 2000s. Their approach of bringing fanless and power-efficient designs to the x86 market was groundbreaking at the time.
VIA processors are designed by Centaur Technology, and there is an excellent documentary entitled "Rise of the Centaur" retracing their history, which I really enjoyed watching.
It's unfortunately very difficult to find information about recent VIA x86 CPUs. The VIA QuadCore, their latest one, was announced in May 2011, and it remains an open question whether there will be newer ones or not, as the company seems to be focusing on the ARM architecture.
In fact, the status of VIA's x86 licensing agreement is quite unclear. There was an FTC ruling against Intel in 2010 specifying that a five years extension should be offered to VIA once the ongoing agreement would expire in 2013, and that the agreement should be modified to allow VIA (among other companies) to consider mergers or joint ventures. The latter being the way VIA apparently took, which gave birth to Zhaoxin.
Some information in English about Zhaoxin x86 CPUs is available on WikiChip. However, those CPUs seem to only be available within China. For now?
Given the current state of affairs on the x86 market (Intel ME, AMD Secure Technology, Meltdown, Spectre) and upcoming vulnerabilities announcements lurking on the horizon, there is definitely a spot for alternative x86 processors.