  In 2013 the Nobel Prize in Physics was awarded to Francois Englert and Peter
Higgs for their development in 1964 of the mass generation mechanism (the Higgs
mechanism) in local gauge theories. This mechanism requires the existence of a
massive scalar particle, the Higgs boson, and in 2012 the Higgs boson was
finally observed at the Large Hadron Collider after being sought for almost
half a century. In this pedagogical article we review the work of these Nobel
recipients and discuss its implications. We approach the topic from the
perspective of a dynamically generated Higgs boson that is a
fermion-antifermion bound state rather than an elementary field that appears in
an input Lagrangian. In particular, we emphasize the connection with the BCS
theory of superconductivity. We identify the double-well Higgs potential not as
a fundamental potential but as a mean-field effective Lagrangian with a
dynamical Higgs boson being generated through a residual interaction that
accompanies the mean-field Lagrangian. We discuss what we believe to be the key
challenge raised by the discovery of the Higgs boson, namely determining
whether it is elementary or composite, and suggest that the width of the Higgs
boson might serve as a suitable diagnostic for discriminating between an
elementary Higgs boson and a composite one.
