The electrical properties of semiconductor surfaces have played a decisive role in one of the most important discoveries of the last century, transistors. In the 1940s, the concept of surface states--new electron energy levels characteristic of the surface atoms--was instrumental in the fabrication of the first point-contact transistors, and led to the successful fabrication of field-effect transistors. However, to this day, one property of semiconductor surface states remains poorly understood, both theoretically and experimentally. That is the conduction of electrons or holes directly through the surface states. Since these states are restricted to a region only a few atom layers thick at a crystal surface, any signal from them might be swamped by conduction through the underlying bulk semiconductor crystal, as well as greatly perturbed by steps and other defects at the surface. Yet recent results show that this type of conduction is measurable using new types of experimental probes, such as the multi-tip scanning tunnelling microscope and the micro-four-point probe. The resulting electronic transport properties are intriguing, and suggest that semiconductor surfaces should be considered in their own right as a new class of electronic nanomaterials because the surface states have their own characters different from the underlying bulk states. As microelectronic devices shrink even further, and surface-to-volume ratios increase, surfaces will play an increasingly important role. These new nanomaterials could be crucial in the design of electronic devices in the coming decades, and also could become a platform for studying the physics of a new family of low-dimensional electron systems on nanometre scales. Ó