Purpose of Review <p>The 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.</p> Recent Findings <p>We 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.</p> Summary <p>We find that there is not a single market design that outperforms the others <i>vis-à-vis</i> all 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.</p>