The lipid bilayer part of biological membranes is a complex lipid mixture displaying cooperative phenomena. By means of differential scanning calorimetry and computer simulation techniques, the equilibrium and non-equilibrium properties of the large assembly of mutually interacting amphiphilic lipid molecules constituting the lipid bilayer have been investigated. The cooperative many-particle lipid bilayer behavior is manifested in terms of phase transitions and large-scale macroscopic phase equilibria. On a smaller nanometer length-scale, equilibrium structural and compositional fluctuations lead to the formation of a heterogeneous lateral bilayer structure composed of dynamic lipid domains and differentiated bilayer regions. In addition, the non-equilibrium dynamic ordering process of coexisting phases can give rise to the formation of local lipid structures on various length- and time-scales. The results suggest that the structural and dynamical lipid bilayer behavior and in particular the appearance of small-scale lipid structures might be of importance for membrane functionality, e.g., membrane compartmentalization, trans-membrane permeability, and the activity of membrane-associated enzymes and proteins.