Phase transitions are ubiquitous in nonliving matter, and recent discoveries have shown that they also play a key role within living cells. Intracellular liquid-liquid phase separation is thought to drive the formation of condensed liquid-like droplets of protein, RNA, and other biomolecules, which form in the absence of a delimiting membrane. Recent studies have elucidated many aspects of the molecular interactions underlying the formation of these remarkable and ubiquitous droplets and the way in which such interactions dictate their material properties, composition, and phase behavior. Here, we review these exciting developments and highlight key remaining challenges, particularly the ability of liquid condensates to both facilitate and respond to biological function and how their metastability may underlie devastating protein aggregation diseases.