  Lacunar spinels with a chemical formula of $AM_4X_8$ form a populous family
of narrow-gap semiconductors, which offer a fertile ground to explore
correlation and quantum phenomena, including transition between Mott and
spin-orbit insulator states, ferro/antiferroelectricity driven by cluster
Jahn-Teller effect, and magnetoelectric response of magnetic skyrmions with
polar dressing. The electronic and magnetic properties of lacunar spinels are
determined to a large extent by their molecular-crystal-like structure. The
interplay of electronic correlations with spin-orbit and vibronic couplings
leads to a complex electronic structure already on the single-cluster level,
which -- together with weaker inter-cluster interactions -- gives rise to a
plethora of unconventional correlated states. This review primarily focuses on
recent progresses in the field of optical, dielectric, and magnetoelectric
properties on lacunar spinels. After introducing the main structural aspects,
lattice dynamics and electronic structure of these compounds are discussed on
the basis of optical spectroscopy measurements. Dielectric and polarization
studies reveal the main characteristics of their low-temperature ferro- or
antiferroelectric phases as well as orbital fluctuations in their
high-temperature cubic state. Strong couplings between spin, lattice, and
orbital degrees of freedom are manifested in singlet formation upon
magnetostructural transitions, the emergence of various multiferroic phases,
and exotic domain-wall functionalities.
