Living cells are spatially organized by compartments that can nucleate, grow, and dissolve. Compartmentalization can emerge by phase separation, leading to the formation of droplets in the cell's nucleo- or cytoplasm, also called biomolecular condensates. Such droplets can organize the biochemistry of the cell by providing specific chemical environments in space and time. These compartments provide transient environments, suggesting the relevance of nonequilibrium physics of droplets as a key to unraveling the underlying physicochemical principles of biological functions in living cells. In this review, we highlight coarse-grained approaches that capture the physics of chemically active emulsions as a model for condensates orchestrating chemical processes. We also discuss the dynamics of single molecules in condensates and the material properties of biological condensates and their relevance for the cell. Finally, we propose wetting, prewetting, and surface phase transitions as a possibility for intracellular surfaces to control biological condensates, spatially organize membranes, and exert mechanical forces. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 15 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.