  Consider a tree network T, where each edge acts as an independent copy of a
given channel M, and information is propagated from the root. For which T and M
does the configuration obtained at level n of T typically contain significant
information on the root variable?
  This model appeared independently in biology, information theory, and
statistical physics. Its analysis uses techniques from the theory of finite
markov chains, statistics, statistical physics, information theory,
cryptography and noisy computation. In this paper, we survey developments and
challenges related to this problem.
