We give a short review of old and recent results on scatterers with transmission eigenvalues of infinite multiplicity, including transparent scatterers. Our examples include potentials from the Schwartz class and multipoint potentials of Bethe - Peierls type. This talk is based, in particular, on the works Grinevich, Novikov ( Comm. Math. Phys. 174, 409-446 (1995), EJMCA 9(4), 17-25 (2021), Russian Math. Surveys 77, 1021-1028 (2022)).