Conventional surface crystallography by low-energy electron diffractio
n (LEED) employs a trial-and-error search controlled at each step by h
uman effort. This trial-and-error approach becomes very cumbersome and
unreliable to solve complex surfaces with a large number of unknown s
tructural parameters. We discuss automatic optimization procedures for
LEED, which combine numerical search algorithms with efficient method
s of determining the diffracted intensities for varying structures. Su
ch approaches can reduce the computer time required for an entire stru
cture determination by many orders of magnitude, while fitting many ti
mes more unknown structural parameters. Thereby, relatively complex st
ructures, with typically 10 adjustable atoms (or 30 adjustable coordin
ates), can be readily determined on today's workstations. These includ
e non-symmetrically relaxed structures, surface reconstructions and ad
sorbate-induced substrate distortions. We also address the theoretical
and experimental requirements for an accurate structural determinatio
n.