Josephson junctions translate quantum phase coherence into an electrical response and underpin superconducting sensors and quantum circuits. In conventional junctions, the barrier acts primarily as a passive weak link; however, when the barrier is a quantum material with its own internal degrees of freedom like magnetism, strong correlations, or switchable polarization, the Josephson effect becomes a sensitive probe of symmetry and many-body physics in the interlayer. Here we review progress in "quantum-material Josephson junctions" (QMJJ), focusing on three rapidly advancing barrier families: (1) magnetic barriers, where exchange, noncollinearity, and spin-active scattering enable 0-π-φ ground states, singlet-triplet conversion, and nonreciprocal transport; (2) correlated barriers, where proximity effects acquire many-body character and recent van der Waals Kagome Mott interlayers exhibit field-free Josephson diode behavior; and (3) ferroelectric and multiferroic barriers, where nonvolatile polarization provides an internal control knob and can produce superconducting memory and memristive dynamics.

2D ferroelectric (FE) materials have opened new opportunities in non-volatile memories, computation and non-linear optics due to their robust polarization in the ultra-thin limit and inherent flexibility in device integration. Recently, interest has grown in the use of 2D FEs in electro-optics, demanding the exploration of their electronic and optical properties. In this work, the discovery of an unprecedented anomalous thickness-dependent change in refractive index, as large as δn ∼ 23.2%, is reported in the 2D ferrielectric CuInP₂S₆, far above the ultra-thin limit, and at room temperature. It is also shown that the anomalous behavior in CuInP₂S₆ may be generalizable to other ferroelectric materials such as LiNbO₃. Furthermore, CuInP₂S₆ exhibits a giant birefringence in the blue-ultraviolet regime, with a maximum |n_OOP − n_IP| ∼ 1.24 at t ∼ 22 nm and λ = 339.5 nm, which is, to the best of our knowledge, the largest of any known material in this wavelength regime. Changes in the optical constants of CuInP₂S₆ are related to changes in the Cu(I) FE polarization contribution, inducing changes in its ionic mobility, and opening the door to electronic control of its optical response for use in photonics and electro-optics.