  We summarize recent progress in lattice studies of four-dimensional N=4
supersymmetric Yang--Mills theory and present preliminary results from ongoing
investigations. Our work is based on a construction that exactly preserves a
single supersymmetry at non-zero lattice spacing, and we review a new procedure
to regulate flat directions by modifying the moduli equations in a manner
compatible with this supersymmetry. This procedure defines an improved lattice
action that we have begun to use in numerical calculations. We discuss some
highlights of these investigations, including the static potential and an
update on the question of a possible sign problem in the lattice theory.
