  We show existence, uniqueness, and directedness properties for infinite
geodesics in the FPP model. After giving the fundamental definitions, we
describe results by Newman and collaborators giving existence and uniqueness of
directed geodesics under an unproven curvature assumption. We then give two
proofs of the existence of at least two infinite geodesics under no unproven
assumptions. In the final two sections, we give proofs of directedness
statements for infinite geodesics using more recent methods which give
information even under no unproven assumptions and prove a generalized
uniqueness statement for infinite geodesics.
