Ferroelectric materials are defined as the materials, of which spontaneous polarization can be switched by an external electric field. Their crystal structural symmetry makes them exhibit a variety of electric properties, such as piezoelectricity, pyroelectricity, and ferroelectricity. Because of their characteristics, they are expected to be adapted for various applications, including sensors, actuators, and non-volatile memories. Over the past decades, perovskite type ferroelectric materials have occupied the central position in both fundamental studies and applications of ferroelectric materials. On the other hand, there are a few studies on ferroelectrics with other crystal structures.This regime is now changing since HfO2-based new ferroelectric materials have been discovered. The HfO2-based dielectric materials are employed as high-k insulators of the metal-oxide-semiconductor field-effect-transistors instead of the conventional SiOx gate dielectrics, suggesting the high compatibility with semiconductor technologies. Thus, discovering ferroelectricity in HfO2-based materials strongly encourages us to develop highly integrated ferroelectric devices that are difficult to fabricate with traditional perovskite-type ferroelectrics. Amid increasing interest in ferroelectric materials, ferroelectricity is demonstrated on another new (Al, Sc)N, which has a wurtzite structure. Both fluorite structure, the parent structure of HfO2-based ferroelectrics, and wurtzite structure are simple compounds, having only a single anion and cation sites in the crystal structure. This feature contrasts the complex crystal structure of conventional perovskite structure. This presentation will give a brief outline of these new ferroelectric materials and introduce our recent studies from the viewpoint of crystal chemistry. It is well-known that HfO2 undergoes successive phase transitions from monoclinic to tetragonal and tetragonal to cubic phases. However, these phases cannot show ferroelectricity because of their inversion center in the crystal structure. It is widely accepted that the ferroelectricity in HfO2-based materials originates from the metastable orthorhombic structure. This orthorhombic structure was confirmed by the convergence electron diffraction and scanning transmission electron microscopy. Among the HfO2-based materials, HfO2- ZrO2 materials are most extensively studied. However, the thickness that can exhibit ferroelectricity in these materials is limited to less than 50 nm because of their strong preference for the monoclinic structure. In order to investigate structural features of the HfO2-based materials, materials are demanded that have ferroelectricity over the wide thickness range. The Y-doped HfO2 meets the requirement, allowing us to grow the ferroelectric film over 1 μm in thickness. Furthermore, we demonstrated ferroelectricity in epitaxial films using this composition. A recent report on ferroelectricity in bulk single-crystal also employed the Y-doped HfO2 system. The ferroelectricity in the wurtzite structure has been discussed for a long time. Moriwake et al. put forward giant spontaneous polarization in wurtzite materials by calculation based on density functional theory. The proposed mechanism of polarization reversal is accompanied by the change in the outermost surface, namely a cation surface to an anion surface and vice versa. Such large polarization was demonstrated in (Al1-x Scx)N films by Fitchtner et al. They also confirmed the change in the surface by performing chemical etching. In addition to (Al1-x Scx)N films, the ferroelectricity has been confirmed in (Al1-x B x )N, (Ga1-x Sc x )N, and (Zn1-x Mg x )O. For the wurtzite structure, we can consider the virtual paraelectric BN phase, in which both anions and cations are located in the same plane. As the paraelectric phase is deemed an intermediate state during polarization reversal, easy polarization reversal is expected as the u-parameter of the wurtzite structure approaches 0.5. It is considered that the u parameter is closely related to the axial ratio of the c- and a-axes. In fact, the reduction of coercive field and remanent polarization is ascertained experimentally. The “simple compound” ferroelectrics have attracted much attention due to their unique features, e.g., outstanding compatibility to semiconductor technologies in HfO2-based materials and giant remanent polarization in wurtzite materials. However, quite a large coercive field compared to conventional ferroelectrics reduces the reliability of the devices, particularly endurance properties. Further studies and developments to unveil microstructures under and after applying a strong electric field will lead to the next application of these ferroelectrics.