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

Topological insulators based on HgTe