  We consider first-passage percolation with i.i.d. non-negative weights coming
from some continuous distribution under a moment condition. We review recent
results in the study of geodesics in first-passage percolation and study their
implications for the multi-type Richardson model. In two dimensions this
establishes a dual relation between the existence of infinite geodesics and
coexistence among competing types. The argument amounts to making precise the
heuristic that infinite geodesics can be thought of as `highways to infinity'.
We explain the limitations of the current techniques by presenting a partial
result in dimensions higher than two.
