I present a concise review of the Higgs problem which plays a central role in
particle physics today. The Higgs of the minimal Standard Model is so far just
a conjecture that needs to be verified or discarded at the LHC. Probably the
reality is more complicated. I will summarize the motivation for New Physics
that should accompany or even replace the Higgs discovery and a number of its
possible forms that could be revealed by the LHCComment: 17 pages, 3 figures, Talk presented at the Corfu Summer Institute:
School and Workshop on the Standard Model and Beyond - Standard Cosmology,
Corfu, Greece, August 31 - September 6, 2009 A few references added