I see several comments here that misunderstand "perovskites", so to be clear: "perovskite" can refer to either the mineral or the crystal structures with the same structure as the mineral. Virtually everything written about "perovskites" refers to perovskite structures; the actual mineral perovskite is just used as a rock (geologists poke at it and miners crush it up.)

Perovskite structures are interesting because they have unique material properties. The range of properties is quite broad: ferroelectric, pyroelectric, and piezoelectric properties, photoelasticity, very high permittivity, et cetera. In popular science news, you will mostly read about potential uses in solar cells, but they are already commonly used in our world: barium titanate is used as a dielectric in capacitors, lead zirconium titanate is used as the piezoelectric crystal in many resonators, lithium niobate is used for optical waveguides and for optical antialiasing filters because of its birefringence.