Protein-rich droplets, such as stress granules, P-bodies, and the nucleolus, perform diverse and specialized cellular functions. Recent evidence has shown the droplets, which are also known as biomolecular condensates or membrane-less compartments, form by phase separation. Many droplets also contact membrane-bound organelles, thereby functioning in development, intracellular degradation, and organization. These underappreciated interactions have major implications for our fundamental understanding of cells. Starting with a brief introduction to wetting phenomena, we summarize recent progress in the emerging field of droplet–membrane contact. We describe the physical mechanism of droplet–membrane interactions, discuss how these interactions remodel droplets and membranes, and introduce “membrane scaffolding” by liquids as a novel reshaping mechanism, thereby demonstrating that droplet–membrane interactions are elastic wetting phenomena. “Membrane-less” and “membrane-bound” condensates likely represent distinct wetting states that together link phase separation with mechanosensitivity and explain key structures observed during embryogenesis, during autophagy, and at synapses. We therefore contend that droplet wetting on membranes provides a robust and intricate means of intracellular organization.