  This text is the preprint version of the concluding chapter for the book New
Directions in Locally Compact Groups published by Cambridge University Press in
the series Lecture Notes of the LMS. The recent progress on locally compact
groups surveyed in that volume also reveals the considerable extent of the
unexplored territories. Therefore, we wish to conclude it by mentioning a few
open problems related to the material covered in the book and that we consider
important at the time of this writing.
