For many years a large, short-range repulsive interaction has been observed between a variety of hydrated surfaces. The physical origin of this ubiquitous interaction has been controversial. In the case of lipid bilayers, proposed mechanisms include a hydration pressure, due to water polarization and/or hydrogen-bond reorientation by the bilayer surface, and several types of entropic (steric) pressures, due to motion of individual lipid molecules or undulations of the entire bilayer. This review focuses on a number of recent osmotic stress/X-ray diffraction experiments performed with phosphatidylcholine bilayers designed to determine the distance range where each of these pressures dominates. At very short interbilayer separations (less than about 4 Angstrom), the pressure-distance curve depends on the volume fraction of head groups at the interface, indicating the presence of a large steric barrier arising from direct interactions between head groups from opposing bilayers. The range of this steric pressure can be increased by the addition of lipids with larger head groups, such as glycolipids or lipids with covalently attached polymers (polyethylene glycol lipids). For intermediate interbilayer separations (about 4-10 Angstrom), the pressure-distance curves are similar for liquid-crystalline and crystalline phosphatidylcholine bilayers, the pressure-fluid spacing relationship is nearly independent of temperature, and the magnitude of the pressure depends on the dipole potential. In this range of fluid spacings we argue that the pressure can be best accounted for by a hydration pressure. For interbilayer spacing greater than about 10 Angstrom, the magnitude and range of the observed pressure depend on temperature and on the bending modulus of the bilayer. These observations provide compelling evidence for the presence of a longer-range undulation pressure, that markedly influences the hydration properties of phospholipid bilayers.