This article surveys several research challenges in interdomain routing. We introduce and describe these challenges in a comprehensible manner, along with a review of the most compelling contributions and ongoing research efforts addressing each of the exposed issues. During this analysis we identify the relation between these research challenges and how they influence each other. We also present our perspectives on why these issues remain largely unsolved, and point out why some of the proposals made so far have not yet been adopted. We hope this can provide some insight on future directions in this complex research area.