  We present a survey of techniques to obtain upper bounds for the variance of
the passage time in first-passage percolation. The methods discussed are a
combination of tools from the theory of concentration of measure, some of which
we briefly review. These are combined with variations on an idea of
Benjamini-Kalai-Schramm to obtain a logarithmic improvement over the linear
bound implied by the Efron-Stein/Poincare inequality, for general edge-weight
distributions.
