The Witsenhausen counterexample has stood as an unsolved problem in
distributed control for over 40 years. It is a seemingly simple
two-stage scalar control problem that has linear dynamics, Gaussian
random variables, and a quadratic cost function. However, nobody could
prove what the optimal strategy is. Unlike many LQG problems, linear
strategies are suboptimal and about ten years ago, it was shown that
the performance gap between linear and nonlinear strategies could be
an arbitrarily high factor. Recently, we have succeeded in casting the
problem as an information-theory problem that emphasizes its implicit
communication aspect --- resulting in arguably the simplest unsolved
problem in information theory since it is basically a point-to-point
problem with one encoder and one decoder. We have a new "converse"
bound for the problem that improves considerably on Witsenhausen's
original bound. Using this bound, for an asymptotic version of the
problem, we can give an approximately optimal strategy whose cost is
always within a factor of two of optimal. Very recently, we have
obtained a similar constant-factor result for the original scalar
Witsenhausen problem itself.