At the beginning of the 21st century, it became obvious that radical changes had taken place in the concept of living matter and, in particular, in the concept of the organization of intracellular space. The accumulated data testify to the essential importance of phase transitions of biopolymers (first of all, intrinsically disordered proteins and RNA) in the spatiotemporal organization of the intracellular space. Of particular interest is the stress-induced reorganization of the intracellular space. Examples of organelles formed in response to stress are nuclear A-bodies and nuclear stress bodies. The formation of these organelles is based on liquid–liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) and non-coding RNA. Despite their overlapping composition and similar mechanism of formation, these organelles have different functional activities and physical properties. In this review, we will focus our attention on these membrane-less organelles (MLOs) and describe their functions, structure, and mechanism of formation.