  In a series of recent preprints, we have proven that with probability one the
Hausdorff dimension on the outer boundary of planar Brownian motion is 4/3,
confirming a conjecture by Mandelbrot. It is also shown that the Hausdorff
dimension of the set of cut points is a.s. 3/4. The present paper is an
expository outline of the arguments involved in the proof of these and related
results.
