It is now established that crystalline cellulose is held together not just by hydrogen bonding, but also by dispersion forces and by electrostatic attraction modulated by stereoelectronic factors such as the exo-anomeric effect. The surface chains of native cellulose microfibrils differ in C6 conformation from crystalline cellulose and therefore form different hydrogen bonds, both outward and inward. Dispersion and electrostatic forces, influenced by cellulose conformation, also operate at the microfibril surface. The surface conformation depends on whether cellulose interacts with water, with the surfaces of other microfibrils or with non-cellulosic polymers. Cellulose-water binding competes with other binding interactions, so that diverse surface interactions are finely balanced in free energy, difficult to simulate, and dependent on local details of water structuring about which little is known, especially in the presence of dispersed chains of hemicellulosic or pectic polymers. An example is the influence of hydration on the aggregation of microfibrils as measured by neutron scattering, which is large for primary-wall cellulose and small for hardwood microfibrils. There are many consequent uncertainties about the surface interactions of hydrated cellulose microfibrils, for example how pectins associate with cellulose or why cellulose-xylan interfaces resist hydration. Evidence from a range of experimental technologies, alongside simulations, will be needed to resolve these uncertainties. The practical implications are wide-ranging, from the mechanism of plant growth and the mechanical resilience of wood to the development of novel, wood-based building materials.