  The concept of topological insulator (TI) has introduced a new point of view
to condensed-matter physics, relating a priori unrelated subfields such as
quantum (spin, anomalous) Hall effects, spin-orbit coupled materials, some
classes of nodal superconductors and superfluid $^3$He, etc. From a
technological point of view, topological insulator is expected to serve as a
platform for realizing dissipationless transport in a non-superconducting
context. The topological insulator exhibits a gapless surface state with a
characteristic conic dispersion (a surface Dirac cone). Here, we review
peculiar finite-size effects applicable to such surface states in TI
nanostructures. We highlight the specific electronic properties of TI nanowires
and nanoparticles, and in this context contrast the cases of weak and strong
TIs. We study robustness of the surface and the bulk of TIs against disorder,
addressing the physics of Dirac and Weyl semimetals as a new perspective of
research in the field.
