*Biased random walk on percolation clusters*

**Abstract:**
We consider biased random walk on
supercritical percolation clusters
in $\bf Z^2$.
We show that the random walk is transient and that
there are two speed regimes: If the bias is large enough,
the random walk
has speed zero, while if the bias is small enough,
the speed of the random walk is positive.Fluctuation exponents and large deviations for directed polymers in a
random environment
(with Y. Hu)