when "in undertaking a review" is used in a conversation to someone , it would imply that the addressee is being asked to embark on a systematic search of the available and accessible literature to compile a document supporting his/her claim or theory. This may vary from subject to subject.
In science this would mean that the practical aspect is to be compiled into a scientific document after taking stock of all published literature on the topic until the current date. The researcher would also have to incorporate his/her work as a new recent development in this area.
In arts however the researcher should delve into the library bookshelves (online and hard) accumulating all the literature there is on the subject. He/she then has the freedom to compile a document on the topic to either publish or to incorporate as a thesis chapter. science doesnt allow you to put reviews as your thesis chapters..(correct me if iam wrong)
BY undertaking a review is a form of reported speech when the author is justifying his findings based on the exhaustive review he/she has prepared ....