Tomb Raider Underworld was the follow-up to the reboot of the Tomb Raider Series, Tomb Raider Legend - (my lp of that is here). Tomb Raider Anniversary was in many ways not really a successor, and the tiny gap between the two - one year - suggests that Underworld was in development simultaneously.
Underworld contains a vastly expanded moveset, new combat moves, a hugely improved and actually quite impressive engine, and motion-captured animations. It looks fantastic.
However, it did not quite wow the critics as it might have done - it averages about 80% on metacritic.
This is for a number of reasons which I'll explore in the LP.
Before watching the LP, I suggest you watch the trailer: