This short note is an advertisement for a new review of topological string theory and its applications by Andy Neitzke and Cumrun Vafa
I think that it is a very well written review of a majority of important aspects of topological A-models and B-models. You know, these are "twisted" versions of string theory whose dynamics is topological both on the worldsheet and spacetime, but they nevertheless know about some holomorphic quantities of the original ("full") string theory. Well, let me not copy their review here.
To be fair and balanced, let's also say that there is a competing review by Marcos Mariňo
Marcos's review is focused on the relation of topological strings with the old matrix models.
You can use this article as space for your general comments about topics in topological string theory and its role in the scheme of things.
See also topological (string/field) theory textbooks.