LG's G Flex is the first phone that uses LG Display's flexible plastic OLED display - a 6" 720p display that is curved from top to bottom. The G Flex is currently only available in Korea. You can wait till LG brings it to the US, but you can also buy it now on Amazon.com - unlocked for $1,150 (that's the Korean model).
The G Flex has a 2.3Ghz Snapdragon S800 CPU, 2GB of RAM, 32GB of internal memory, a 13MP camera, NFC, Android 4.2.2 and a 3500mAh non-removable battery (LG Chem's curved battery). The G Flex has two rear-mounted buttons and a "self-healing" back (that will heal scratches quickly).