The main components of the cell membrane are the phospholipids, which arrange themselves in a bilayer.
Some phospholipid hydrophobic tails are unsaturated which can increase membrane fluidity.
Animal cells can communicate through their extracellularmatrix and through the junctions between them. Junctions allow communication between animal cells. Adhesion junctions mechanically attach adjacent cells. Tight junctions are another type of adhesion junctions that bring cells even closer than desmosomes. A gap junction allows cells to communicate.
In a plant, the cytoplasm of living cells is connected by plasmodesmata, numerous narrow, membrane-lined channels that pass through the cell wall allowing cell communication.