Researchers have been saying for years and years that reading an on LCD screen late at night will disrupt your sleep, and techies have been working nearly as long to come up with fixes for that problem.
There are two general solutions to the problem (three, if you count not using your device within two hours of going to bed). One is called a night reading mode, and the other is using the software settings to apply a blue light filter to the screen.
One common solution offered by many reading apps is to invert the colors so that the text is white on a black background. It's called a night reading mode, and you can find it in most reading apps such as Kindle, iBooks, Aldiko, Kobo, etc, and looks something like this:
The night reading mode is not unpopular with ebookophiles, but I'm not sure that it really counts as a solution to the sleep problem.
Anecdotal reports suggest that it might help (some users swear by it) but the only true solution would be to use a blue light filter.
Study after study has shown that the blue light emitted from a screen can impact your sleeping patterns. Why blue and not any other color? I don't know the answer to that, but I can say that it's what everyone is saying and it is where all the app developers are turning their attention.
If you like to read or work on your PC late at night then you should look at an app called f.lux. It adjusts the color settings on your monitor based on the local time for your location. You can also set the filter manually, but the automatic setting looks a lot like the Oyster demo above.
And most importantly, it changes the color settings on a system level. So if you install F.lux, it will affect all the apps you use and make them look different.
The F.lux app for Windows comes so highly recommended that I've not heard of an alternative. But I can't make the same remark about Android.
In December 2015 Amazon released an update to Fire OS Bellini which added a blue light filter called Blue Shade. This feature is only available on the latest model year Fire tablets, and you can see screenshots here.
Update: Google added a blue light filter to Google Play Books in late December 2015.
A quick search of Google Play reveals that there are countless free apps which claim to offer a blue light filter, but I'm not so sure how true that is.
I've checked a half-dozen, and many simply turn down the backlight and apply a grey, and not blue, filter. There are a few apps which do apply a color filter, and some even offer alternate color options for the filter (here's one).
Edit: One app in particular, Twilight, has been recommended several times in the comment section of this post. I'd try that first.
You have far fewer options for late night reading on your iPad or iPhone. There's the Oyster app mentioned above and the night reading mode in ebook apps, I only found a few options for iOS. Opera, for example, just updated their browser with a night reading mode and a blue light filter, but there's no general solution.
Edit: But there is Google Play Books.
I'd bet that the lack of options stems from Apple not letting apps mess with the system settings. And that means we'll just have to wait for Apple to discover this problem and decide to decide to solve it.
Not having other devices to check, I can't tell you whether you can find blue light filters on other platforms.
If you use one, let us know in the comments. I'm sure I won't be the only one who is interested.