  We survey the state-of-the-art knowledge of ferroelectric and ferroelastic
group-IV monochalcogenide monolayers. These semiconductors feature remarkable
structural and mechanical properties, such as a switchable in-plane spontaneous
polarization, soft elastic constants, structural degeneracies, and
thermally-driven two-dimensional structural transformations. Additionally,
these 2D materials also display selective valley excitations, valley Hall
effects, and persistent spin helix behavior. After a description of their Raman
spectra, a discussion of optical properties arising from their lack of
centrosymmetry---such as an unusually strong second-harmonic intensity, large
bulk photovoltaic effects, photostriction, and tunable exciton binding
energies---is provided as well. The physical properties observed in these
materials originate from (correlate with) their intrinsic and switchable
electric polarization, and the physical behavior hereby reviewed could be of
use in non-volatile memory, valleytronic, spintronic, and optoelectronic
devices: these 2D multiferroics enrich and diversify the 2D materials toolbox.
