In multicellular organisms, interactions between cells and intercellular communications form the very basis of the organism’s survival, the functioning of its systems, the maintenance of homeostasis and adequate response to the environment. The accumulated experimental data point to the particular importance of intercellular communications in determining the fate of cells, as well as their differentiation and plasticity. For a long time, it was believed that the properties and behavior of cells were primarily governed by the interactions of secreted or membrane-bound ligands with corresponding receptors, as well as direct intercellular adhesion contacts. In this review, we describe various types of other, non-classical intercellular interactions and communications that have recently come into the limelight—in particular, the broad repertoire of extracellular vesicles and membrane protrusions. These communications are mediated by large macromolecular structural and functional ensembles, and we explore here the mechanisms underlying their formation and present current data that reveal their roles in multiple biological processes. The effects mediated by these new types of intercellular communications in normal and pathological states, as well as therapeutic applications, are also discussed. The in-depth study of novel intercellular interaction mechanisms is required for the establishment of effective approaches for the control and modification of cell properties both for basic research and the development of radically new therapeutic strategies.