The rules that determine which assets count as eligible collateral for central bank operations, and at what haircuts, are not just operational details. They have become a first-order determinant of asset prices, liquidity allocation, and financial stability. This review synthesizes the literature on three transmission channels: convenience yield, collateral scarcity, and market liquidity. I trace the intellectual lineage from Singh and Stella (2012) through Williamson (2016) to the empirical studies of Nyborg and Woschitz (2021), Lengwiler and Orphanides (2024), and Fang, Wang, and Wu (2020). My central argument is that this literature, taken as a whole, reveals a fundamental policy trilemma. Central banks must choose among unconditional acceptance of their own government’s debt (which risks fiscal dominance), rating-based eligibility (which risks self-fulfilling sovereign crises), and discretionary policy-driven eligibility (which risks politicization). No design is safe. I also identify four open questions: the nonlinearity of the collateral channel, its interaction with bank portfolio behavior, the systemic risk of cliff effects, and the external validity of evidence from China.