I have developed a theory of contact mechanics and adhesion between elastic solids with randomly rough surfaces. The theory takes into account that partial contact may occur between the solids on all length scales. The theory predicts how the area of real contact, the stress distribution in the contact regions and the distribution of interfacial separations depends on the load. The theory is very flexible and can be applied to both elastic and viscoelastic solids with or without adhesion. Plasticity effects can also be easily included in the theory. As an illustration, I discuss the leak-rate of seals, adhesion and bioadhesion.