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Abstract Purpose of ReviewThe share of asynchronous inverter-based resources is increasing in many electricity systems, displacing synchronous generators. This leads to a decreasing level of system inertia, which threatens electricity-system stability. This dynamic raises the question of how to secure sufficient levels of inertia. One possibility is taking a market-based approach to incentivize the installation of inertia-providing equipment. To this end, this paper reviews market designs to reimburse inertia provision that are discussed in the literature. Recent FindingsWe find five distinct market designs to remunerate inertia that are discussed in the literature—bilateral negotiation, tendering, auctions, bonus systems, and integrating inertia-related constraints into energy-market models. In addition, there are other approaches that are not based on a market mechanism—penalties, regulatory obligations, self-provision by electricity-system operators, and redispatch. We examine current approaches that are employed by Ireland, Great Britain, Australia, and Germany, which demonstrate the real-world use of these theoretical designs. We assess the five market designs based on their advantages and disadvantages. SummaryWe find that there is not a single market design that outperforms the othersvis-à-visall market-performance indicators. Which market design is suited best for a specific use case depends upon the particular circumstances. A solely market-based solution may not be sufficient to secure electricity-system stability and should be enriched with regulatory guidelines to mitigate the risk of market failure.