There are various apps on Android that promise to alter the color temperature of your screen at night to promote better sleep, but the popular desktop app f.lux has thus far not been among them. This is about to change, though. A beta version of f.lux for Android is available for download right now, but it does require root.
The idea behind apps like f.lux and Twilight is that the blue light emitted by your screen sends signals to your brain that make it think the sun is out. This can interfere with your ability to sleep if you use a phone in the evening. So, these apps try to shift the screen to a warmer temperature to reduce that effect.
Apps like Twilight simply add a red filter on top of the UI, which may or may not be effective—it kind of depends on who you ask. f.lux needs root because it's actually intercepting the pixels from the GPU and desaturating the blues. This should be more effective, but again, it depends who you ask. To get into the beta, you'll have to sign up for the f.lux forums and ask to be added to the test.