Kyocera isn't exactly a big name in modern Android smartphones, but it does make a lot of rugged devices that don't get much press. It's also big in materials science, which is where sapphire comes in. See, it seems like a safe bet that the next iPhone will have a sapphire glass display, and Kyocera happens to know a lot about manufacturing synthetic sapphire for watches and electrical components. So, they're making sapphire screens for smartphones.
As a keen and professional observer of the modern consumer electronics market, I can say without fear of contradiction that smartphone screens are getting bigger. So can columnist Alex Barredo, but he's done an impressive amount a statistical legwork and presentation to prove it. On the surface his analysis of smartphone size screen trends may seem obvious, but within you can find dramatic shifts in patterns of both the overall market and specific companies.
Phones are always getting thinner. For whatever reason, that's a metric that matters to the general public more than battery life. As the phones slim down, so do the screens. LG is stepping up its display game by producing the thinnest 1080p LCD in the world. This 5.2-inch panel is only 2.2mm thick and has a 2.3mm bezel. This is about as svelte as you can make a bezel without getting into those wacky bending screens that pop up at tradeshows, but never in actual devices.