  Quantum impurity problems in Tomonaga-Luttinger liquids (TLLs) are reviewed
with emphasis on their analogy to the Kondo problem in Fermi liquids. First,
the problem of a static impurity in a spinless TLL is considered, which is
related to the model studied in the context of the macroscopic quantum
coherence. In the low-energy limit the TLL is essentially cut into two pieces
when interaction is repulsive. The orthogonality catastrophe in a TLL is then
discussed. Finally, the Kondo effect of a spin-1/2 impurity in a
one-dimensional repulsively interacting electron liquids (a spinful TLL) is
reviewed. Regardless of the sign of the exchange coupling, the impury spin is
completely screened in the ground state. The leading low-temperature
contributions to thermodynamic quantities come from boundary contributions of a
bulk leading irrelevant operator.
