The Kondo effect is a well-known phenomena that there is an enhancement of the electric resistance of electrons in metal containing impurity atoms with finite spin at low temperature. The conditions of the emergence of the Kondo effect are summarized as (i) Fermi surface (degenerate state) (ii) loop effect (particle-hole creation) and (iii) non-Abelian interaction. Those conditions can be satisfied for nuclear matter and quark matter where heavy hadrons and quarks are contained as immunity particles in the medium. In this presentation, I will introduce the recent studies of the Kondo effects in nuclear matter and quark matter, whose results may be studied in experiments in J-PARC, GSI-FAIR, NICA as well as in RHIC and LHC.