Highlights and Shadows
Whilst the exposure controls control the mid-tones, the Highlights and Shadows controls work on these ends of the tone range. In addition the Whites and Blacks controls adjust the upper and lower limits of the brightness range – this is particularly relevant where you are using Raw files, where the file contains the full tonal range the sensor can capture, which is generally much greater than the screen or printer can display. Using these controls you can bring out detail in what initially looks like black shadow areas, and recover detail in overblown highlights.
Consider the following image. Here we have a scene with huge dynamic range. To try to get detail in the whites of the water fall, the image looks underexposed
Boosting the exposure slider 1.5 stops gives better exposure of the forest, but the water is now overexposed and lacks detail
Dragging the highlights slider down restores detail in the water.
Boosting shadows gives more detail in the shadows under the cliff, and adding some clarity and dehaze filter and some vibrance gives the resulting image more punch.
These controls can also be useful more creatively, if you want to make an image more dramatically contrasty, by decreasing the shadows to make a darker, more moody effect, or boosting the highlights for a high-key look.
In some software you may find a dehaze control which also adjusts tonality, in particular reducing blue luminosity (haze tends to be bluish) and increasing contrast. These controls can be fantastic for cutting through haze, but might also be of value in other situations too. Twiddle the control and see what the effects are on your images.
Often, as in Photoshop, there are advanced options on these controls that fine tune how the effects apply. The best way to learn about these controls is to experiment with your own software on a variety of your own images. Have fun.
Here are some links for further reading: