Integrating renewable power generation into existing energy systems is high on the agenda of most developed countries around the world, also aiming to do in a liberalized electricity market environment. Even though liberalized, electricity markets take the form of centralized mechanisms using basic supply-demand equilibrium principles for clearing and price formation. Owing to the very nature of renewable power generation, with inherent variability and uncertainty, also with latent space-time dependencies, this induces a number of challenges in the design and operation of electricity markets. We will introduce and discuss a number of these problems, considering problem definition, state of the art, and some of our proposals. This will first include market coordination problems, e.g., day-ahead and balancing stages, or coordination of markets for electricity and other energy carriers. We will then drift towards offering strategies for renewable power producers in electricity markets, from price-taker to price setter, but also extending to population games. Finally, we will introduce the basic idea of peer-to-peer electricity markets (which do not exist yet, but we expect this to happen soon!) with the desirable properties. These may for instance allow for product differentiation, localization and colouring of exchanges on the grid, etc. The need for new methodologies to account for grid costs, for negotiation and clearing in such decentralized markets, will be detailed.