I've been hearing this phrase for quite a few years now: the anthropocene.
This Guardian piece is an excellent long read on the different conceptions of this era. Not all scientists use the same phrase, and not all agree that we are in fact in this new era.
Gaia Vince's book is an essential resource here.
This David Matless piece is also well worth a read.
It uses a phrase I like: Anthroposcenic: the landscapes of the Anthropocene.
This recent article suggests we are leaving our mark in the fossil record - and not in a good way...