Survey on Erdős-Pósa?
I don't know about a survey, but I've found a recent PhD thesis, which seems to be well written:
Heinlein, Matthias (2019): Erdős-Pósa properties. Open Access Repositorium der Universität Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-11828
The first chapter gives a summary of the problem, known proof techniques and provides references to recent research. I am not an expert on this problem and only skimmed the first chapter briefly, so YMMV.