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Although the specific structures of electricity markets are diverse around the world, they were all conceived on the premise of predictable, controllable generation with nonnegligible marginal costs. Recent changes, specifically, the increasing renewable integration, have challenged such assumptions. In light of this shift, this thesis intends to devise new frameworks and advance our understanding of the future markets. The first part focuses on mechanism design when the model fully reflects the physics of the grid and the participants. We consider a market that involves continuous goods, general nonconvex constraints, and second stage costs. We then design the payments and conditions under which coalitions cannot influence the outcome. Under the incentive-compatible VCG mechanism, we prove that coalition-proof outcomes are achieved if bids are convex and constraints are polymatroids. By relaxing incentive-compatibility, we investigate core-selecting mechanisms that are coalition-proof without conditions. We show that they generalize the economic rationale of the LMP mechanism, and can approximate truthfulness without the price-taking assumption. Finally, they are budget-balanced. The second part coordinates regional markets to exploit the geographic diversification of renewables. In Europe, reserves remain an exclusive responsibility of regional operators. This limited coordination and the sequential structure hinder the utilization of generation and transmission. To promote reserve exchange, a preemptive model can optimally withdraw inter-area transmission capacity from day-ahead energy for reserves. This bilevel program however does not suggest costs that guarantee coordination. We formulate a new preemptive model that allows us to obtain stable benefits immune to deviations. Our proposal, least-core benefits, achieves minimal stability violation with a tractable computation.