In an introductory part I will discuss the relation between
topological insulators and the architectural challenge of
building a bridge between Hongkong and mainland China.
Then I discuss how a magnetic field induces one-dimensional
edge channels when the two-dimensional surface states of
three-dimensional topological insulators become gapped.
Remarkably, the Hall effect remains quantized even in
situations, where the theta-term characteristic of the
bulk and the associated surface Hall conductivities are
not quantized due to the breaking of time-reversal symmetry.
The quantization arises as the theta-term changes by integer
multiples along a loop around n edge channels. Model
calculations show how an interplay of orbital and Zeeman
effects leads to quantum Hall transitions, where channels
get redistributed along the edges of the crystal. The network
of edges opens new possibilities to investigate the coupling
of edge channels. In a last part I will shortly discuss
aspects of strongly disordered topological insulators as well
as interaction effects on the surfaces.