We review the state of the sovereign debt literature and point out that the canonical model of sovereign debt cannot be easily reconciled with several facts about sovereign debt pricing and servicing. We identify and classify more than 20 puzzles. Some are well-known and documented, others are less so and are sometimes based on anecdotal evidence. We classify these puzzles into three categories: puzzles about how sovereigns issue debt; puzzles about the pricing of sovereign debt; and puzzles about sovereign default and the working out of defaults. We conclude by suggesting possible avenues for new research aimed at reconciling theory with what we observe in the real world.