  The most interesting experimental results obtained in studies of 2D and 3D
topological insulators (TIs) based on HgTe quantum wells and films are
reviewed. In the case of 2D TIs, these include the observation of nonlocal
ballistic and diffusion transport, the magnetic breakdown of 2D TIs, and an
anomalous temperature dependence of edge-channel resistance. In 3D TIs, a
record-setting high mobility of surface two-dimensional Dirac fermions (DFs)
has been attained. This enabled determining all the main TI parameters (the
bulk gap and the density of DFs on both of its surfaces) and provided
information on the phase of the Shubnikov - de Haas oscillations of DFs, which
indicates the rigid topological coupling between the fermion spin and momentum.
Prospects for further research are discussed in the conclusion.
