Depends on what is meant by "
fully understood". We do not have a theory of everything yet so nothing can be fully understood.
Usually what happens is that we have a bunch of neat ideas work very well, extremely in some cases.
When someone asks for an explanation we do need some consensus about what counts as an "explanation" for that person.
For instance, iirc the dminant effect re slipping on ice is thought to be to do with surface water on the ice - the probem under investigation is how that water gets there when the temperatures are very low: see overview -
http://dujs.dartmouth.edu/2013/04/what-causes-ice-to-be-slippery/#.V9O-LKJ97VM
... add that you know you can get stuck to ice, and you can wear shoes with lots of little spikes to help you walk on ice, so the physics of slipping over can get complicated.
But weren't you asking about the physics of slipping over at all - on any surface, not just ice?
Like you can slide on concrete flooring, especially if it is polished, especially if you are in socks ... concrete is not a liquid, so that does not work.
Is your question about slipping itself or about how friction works at the microscopic level or what?
The goalposts seem to be moving about. Please pose a coherent question and stick to it.