For most intracellular structures with larger than molecular dimensions, little is known about the connection between underlying molecular activities and higher order organization such as size and shape. Here, we show that both the size and shape of the amphibian oocyte nucleolus ultimately arise because nucleoli behave as liquid-like droplets of RNA and protein, exhibiting characteristic viscous fluid dynamics even on timescales of < 1 min. We use these dynamics to determine an apparent nucleolar viscosity, and we show that this viscosity is ATP-dependent, suggesting a role for active processes in fluidizing internal contents. Nucleolar surface tension and fluidity cause their restructuring into spherical droplets upon imposed mechanical deformations. Nucleoli exhibit a broad distribution of sizes with a characteristic power law, which we show is a consequence of spontaneous coalescence events. These results have implications for the function of nucleoli in ribosome subunit processing and provide a physical link between activity within a macromolecular assembly and its physical properties on larger length scales.