In the physical sciences, solid, liquid, and gas are the most familiar phase states, whose essence is their existence reflecting the different spatial distribution of molecular components. The biological molecules in the living cell also have differences in spatial distribution. The molecules organized in the form of membrane-bound organelles are well recognized. However, the biomolecules organized in membraneless compartments called biomolecular condensates remain elusive. The liquid-liquid phase separation (LLPS), as a new emerging scientific breakthrough, describes the biomolecules assembled in special distribution and appeared as membraneless condensates in the form of a new "phase" compared with the surrounding liquid milieu. LLPS provides an important theoretical basis for explaining the composition of biological molecules and related biological reactions. Mounting evidence has emerged recently that phase-separated condensates participate in various biological activities. This article reviews the occurrence of LLPS and underlying regulatory mechanisms for understanding how multivalent molecules drive phase transitions to form the biomolecular condensates. And, it also summarizes recent major progress in elucidating the roles of LLPS in chromatin organization and provides clues for the development of new innovative therapeutic strategies for related diseases.