  {We give a short review of old and recent results on scatterers with
transmission eigenvalues of infinite multiplicity, including transparent
scatterers. Historically, these studies go back to the publications: Regge
(Nuovo Cimento 14, 1959), Newton (J. Math. Phys. 3, 1962) and Sabatier (J.
Math. Phys. 7, 1966). Our review is based on the works: Grinevich, Novikov
(Commun. Math. Phys. 174, 1995; Eurasian Journal of Mathematical and Computer
Applications 9(4), 2021; Russian Math. Surveys, 77(6), 2022). Results of the
first of these works include examples of transparent at fixed energy potentials
from the Schwartz class in two dimensions. The two others works include the
result that, for compactly supported multipoint potentials of Bethe - Peierls -
Thomas type in two and three dimensions, any positive energy is a transmission
eigenvalue of infinite multiplicity.
