Coalition formation studies the problem of partitioning a given set of agents into different coalitions, where agents have preferences over the other members in their coalition. Typically, the goal is to find a stable outcome, i.e., an outcome where no agent or group of agents has an incentive to deviate to improve their coalition. Despite its simplicity, this model has been extensively studied in multi-agent systems and finds applications in various economic, political, and social processes.

In this talk, I will survey two "recent" developments in the (theoretical) study of coalition formation. One major research challenge is that stable outcomes oftentimes fail to exist and finding them tends to be computationally intractable. Motivated by this, the search for practically relevant subclasses that allow for the compact representation of agent's preferences and the efficient computation of stable outcomes has flourished in recent years.

A second challenge is that most studied models are static in two dimensions. The focus is on finding a stable outcome to be implemented by a central planner and not on the process of forming this outcome. Further, it is assumed that the preferences of agents are static and do not change over time. I will give an overview of the study of dynamic coalition formation which analyzes how stable outcomes form through decentralized individual decisions and how this process might be influenced by a changing perception of other agents.