In this Colloquium the theory of silicon nanowires is reviewed. Nanowires with diameters below 10nm are the focus, where quantum effects become important and the properties diverge significantly from those of bulk silicon. These wires can be treated within electronic structure simulation methods and will be among the most important functional blocks of future nanoelectronic devices. First, the structural properties of silicon nanowires are reviewed, emphasizing the close connection between the growth orientation, the cross section, and the bounding facets. Second, the electronic structure of pristine and doped nanowires is discussed, which holds the ultimate key for their applicability in novel electronic devices. Finally, transport properties are reviewed where some important limitations in the performances of nanowire-based devices can lay. Many unique properties of these systems are at the same time defying challenges and opportunities for technological advances.

Discrete changes of conductance of the order of G₀ = 2e²/h reported during the unipolar reset transitions of Pt/HfO₂/Pt structures are interpreted as the signature of atomic-size variations of the conducting filament (CF) nanostructure. Our results suggest that the reset occurs in two phases: a progressive narrowing of the CF to the limit of a quantum wire (QW) followed by the opening of a spatial gap that exponentially reduces the CF transmission. First principles calculations show that oxygen vacancy paths in HfO₂ with single- to few-atom diameters behave as QWs and are capable of carrying current with G₀ conductance.

Wave-like heat propagation is shown to emerge as a consequence of a rapidly varying temperature field in Ge.