  The quest for $\mu \to e \gamma$ is one of the most important endeavors to
search for New Physics beyond the Standard Model. In this talk I will review
the current status of the experimental searches by the MEG Collaboration at
PSI. I will also present a study of the experimental limiting factors that will
define the ultimate performances, and hence the sensitivity, in the search for
$\mu \to e \gamma$ with continuous muon beams of extremely high rate (one or
even two orders of magnitude larger than the present beams), whose construction
is under consideration for the next decade.
