I found that when using my Android phone for reading webpages reading is often made unnecessarily straining due to the combination of background and foreground color used by websites. Using anything other than black text on white background reduces the effective contrast. In outdoor usage I thus have to increase screen brightness to maximum or even give up reading if I don't want to strain my eyes to the point of painfullness, where a simple black-on-white design would have allowed convenient reading.
Sadly, smartphones (judging from my quick google search, including iphones) reduce tools for screen calibration to the brightness setting. Even the apps I found for doing adjustments on Android were actually counterproductive; E.g. ScreenAdjuster allows reducing but not increasing contrast.
An improvement would be e.g. a way to overwrite the color settings of webpages forcing text to be black, background to be white, but while my preinstalled browser (seems to be some modification of chrome) has an inverse color mode with inproved contrast, I have yet to find a way to increase contrast without inverting colors (which I find even more straining).
Considering that I suffer only very slight short-sightedness I can imagine that while a convenience issue to me it might be a major accesibility issue for others.
On the desktop I'd usually use gamma-correction. It allows to squeeze some more perceived quality out of average screens, e.g. by increasing gamma for dark scenes and decreasing it for bright scenes, improving the effective contrast of the colors currently most prominent on the screen. Likewise, when a desktop program uses fine near-white shades for emphasis of text elements, a gamma adjustment can help. On Smartphones there doesn't seem to be a user-accesible gamma setting however.
PS: On google I have seen many answers along the lines of "increase the brightness". Thus I want to emphasize again: I want to improve the contrast at constant (usually already maximized) screen brightness.