The evolution of the complexity of structural determination attainable
with LEED is reviewed. Considerable progress in methodologies and com
puters has enabled structures as complex as Cu(100) + (4 x 4)-10Li to
be solved in terms of 18 fit parameters. The Si(111)-(7 x 7) structure
could now be refined in terms of 100-or-so fit parameters, if a large
-enough experimental dataset were available. Big challenges remain: fi
nding a direct or quick way to identify the one qualitatively correct
structure; and, to a lesser degree, providing the required size of the
experimental dataset.