Friction affects many aspects of everyday life and has played a central role in technology dating from the creation of fire by rubbing sticks together to current efforts to make nanodevices with moving parts. The friction "laws" we teach today date from empirical relationships observed by da Vinci and Amontons centuries ago. However, understanding the microscopic origins of these laws remains a challenge. One common assumption is that friction is proportional to the true area of contact between surfaces, and Amontons' laws follow because this area is proportional to load. Recent analytic and numerical results for continuum models will be presented to support this view. The contact area and interfacial stiffness are proportional to load, with prefactors that follow from simple dimensional analysis. The remainder of the talk will provide an overview of the challenges in extending the concept of contact to atomic scales and in identifying mechanisms that lead to a simple, robust proportionality between friction and load. Atomic simulations of single asperities and self-affine surfaces are used to test the applicability of continuum theory at atomic scales and the effect of atomic structure on macroscopic forces. Atomic structure has little effect on normal forces, but can change the lateral stiffness and friction by orders of magnitude. At zero temperature, the contact area on bare surfaces is often a factor of two higher than continuum predictions. Thermal fluctuations make it difficult to extend the concept of contact to atomic scales at finite temperature. Most atoms spend most of their time out of contact until the pressure exceeds the bulk yield stress. A rich variety of frictional behaviour can arise, with friction proportional to load, area or neither. Adding a single monolayer of adsorbed molecules changes the contact area dramatically, but leads to a simple proportionality between friction and load.