Two-dimensional (2D) ferroelectric materials offering a combination of semiconductor properties and non-volatile memory properties at the nanoscale, have recently shown great potentials for applications with enhanced integration in electronic and optoelectronic devices, energy harvesting, and electro-mechanical systems. The laminar structure of 2D ferroelectrics guarantees the atomic-layer cleavability, providing an ideal platform for exploring ferroelectricity at the ultrathin limit theoretically and experimentally. In consideration of the low-temperature bottleneck in burgeoning 2D magnetism, 2D ferroelectricity opens up the practical approaches at higher temperature. In this article, we reviewed a kind of laminar materials exhibiting room-temperature stable switchable ferroelectricity, copper indium thiophosphate (CuInP2S6), the potential of which to excavate new science and technology has awakened considerable research interest. The observed high Curie transition temperature, the significant piezoelectric responses, the giant negative piezoelectricity and tunable quadruplewell piezoelectricity, together with the potential of atomic-scale CuInP2S6 films for the novel ferroelectric polarization-based devices, are all demonstrated. A brief introduction about the other typical materials belonging to the transition metal thiophosphate (MIMIIIP2(S/Se)6) compounds family is also involved. The future directions for 2D ferroelectricity research are finally discussed.