I will discuss geodesics in first-passage percolation, a model for fluid flow in a random medium. There are numerous conjectures about the existence, coalescence, and asymptotic direction of infinite geodesics under the model´s random metric. Prior progress on these questions has been made under strong assumptions by Newman and collaborators, with partial results under general assumptions by Häggström/Pemantle and others. I will explain recent results with Michael Damron which develop a framework for addressing these questions; this framework allows us to prove forms of the conjectures under minimal assumptions.