  I review theoretical ideas and implications of experiments for the gap
structure and symmetry of the Fe-based superconductors. Unlike any other class
of unconventional superconductors, one has in these systems the possibility to
tune the interactions by small changes in pressure, doping or disorder. Thus,
measurements of order parameter evolution with these parameters should enable a
deeper understanding of the underlying interactions. I briefly review the
"standard paradigm" for $s$-wave pairing in these systems, and then focus on
developments in the past several years which have challenged this picture. I
discuss the reasons for the apparent close competition between pairing in s-
and d-wave channels, particularly in those systems where one type of Fermi
surface pocket -- hole or electron -- is missing. Observation of a transition
between $s$- and $d$-wave symmetry, possibly via a time reversal symmetry
breaking "$s+id$" state, would provide an importantconfirmation of these ideas.
Several proposals for detecting these novel phases are discussed, including the
appearance of order parameter collective modes in Raman and optical
conductivities. Transitions between two different types of $s$-wave states,
involving various combinations of signs on Fermi surface pockets, can also
proceed through a ${\cal T}$-breaking "$s+is$" state. I discuss recent work
that suggests pairing may take place away from the Fermi level over a
surprisingly large energy range, as well as the effect of glide plane symmetry
of the Fe-based systems on the superconductivity, including various exotic,
time and translational invariance breaking pair states that have been proposed.
Finally, I address disorder issues, and the various ways systematic
introduction of disorder can (and cannot) be used to extract information on gap
symmetry and structure.
