What's the bleeding-edge model for how Population III stars are born and evolve? I'm trying to do a brief literature review to find out what the best current models for population III stellar evolution are. I was hoping that someone with more expertise in the area could perhaps summarise or point me in the right direction.

This post on physics.SE is a great intro, but it's now over 4 years old. 

Recent observations (see here and here) suggest hints of these kinds of stars at relatively low redshift (z ~ 6) - does this provide significant tension on current models? Have there been other observational hints?
This is a more recent review http://arxiv.org/abs/1209.4688 from someone hoping to understand population III by observing their supernovae

Since CR7 was discovered, there's been a bunch of papers on whether it could be pop III - http://arxiv.org/abs/1506.07173 for example. Try searching for "CR7 population III".