  Cell plasma membranes display a dramatically rich structural complexity
characterized by functional sub-wavelength domains with specific lipid and
protein composition. Under favorable experimental conditions, patterned
morphologies can also be observed in vitro on model systems such as supported
membranes or lipid vesicles. Lipid mixtures separating in liquid-ordered and
liquid-disordered phases below a demixing temperature play a pivotal role in
this context. Protein-protein and protein-lipid interactions also contribute to
membrane shaping by promoting small domains or clusters. Such phase separations
displaying characteristic length-scales falling in-between the nanoscopic,
molecular scale on the one hand and the macroscopic scale on the other hand,
are named mesophases in soft condensed matter physics. In this review, we
propose a classification of the diverse mechanisms leading to mesophase
separation in biomembranes. We distinguish between mechanisms relying upon
equilibrium thermodynamics and those involving out-of-equilibrium mechanisms,
notably active membrane recycling. In equilibrium, we especially focus on the
many mechanisms that dwell on an up-down symmetry breaking between the upper
and lower bilayer leaflets. Symmetry breaking is an ubiquitous mechanism in
condensed matter physics at the heart of several important phenomena. In the
present case, it can be either spontaneous (domain buckling) or explicit, i.e.,
due to an external cause (global or local vesicle bending properties). Whenever
possible, theoretical predictions and simulation results are confronted to
experiments on model systems or living cells, which enables us to identify the
most realistic mechanisms from a biological perspective.
