Ghrist has one nice overview article, another one comes from Gunnar Carlsson and his group at Stanford, http://comptop.stanford.edu/preprints/topologyAndData.pd

Ghrist has one nice overview article, another one comes from Gunnar Carlsson and his group at Stanford, http://comptop.stanford.edu/preprints/topologyAndData.pdf http://comptop.stanford.edu/preprints/topologyAndData.pdf (and a toy: http://www.stanford.edu/~gurjeet/mapper.html http://www.stanford.edu/~gurjeet/mapper.html), but you surely know that already. Sorry for I won't attempt to survey literature as this area is new for me too, and I don't want to confuse you, or embarass myself =) I was sure you will find these anyway. I just began dusting off my Morse theory and handful of other mathematics and I am not yet paying much attention to what present developments are directed at. One unfortnate aspect of strictly applied part of this field is that most of results and a leading conference are funded by DARPA, which leads to publications I would consider mostly recruiting material than a scientific communication. My background and goals are anyways disparate to most of the approaches so I took only cursory look.