This photo of my niece Maya was shot in my sister's living room, which, believe it or not, had light walls. Because the room was so large and Maya was standing in a shaft of direct sunlight, not enough light bounced off the walls to lighten the rest of the room. The result: a dramatic portrait of a confident young woman.
There are photographers who are almost obsessed with shadow detail. They buy cameras based on the dynamic range they can deliver. They use tripods, low-flare lenses, and shoot at the lowest available ISO. They bracket like hell, just to make sure they've got at least one "perfect" exposure. Needless to say, they always shoot RAW files, then process them, often with HDR software, to wring out the very last iota of tonal range. Their results are--and I say this without an ounce of sarcasm--very often impressive. The trick, of course, is for the details in those shadows to be worth looking at.
Personally, I have a hell of time managing that feat. What I do instead is to let the shadows fall where they may. I might even darken them to the point where they're solid black. If the shadows are geometric this converts them to graphic compositional elements that serve as negative space that naturally attracts the eye to the the brighter, more colorful areas. That's the idea anyway. Go too far and you end up with a big black mess.
If you'd like to try this for yourself, here are two tips: First, keep in mind that the eye naturally moves to the brighter areas of the image first. Try to develop a sense for whether the detail in the shadows adds or distracts from the highlight detail. If the latter, try adjusting the contrast curve or shadow/black sliders to darken the shadows just enough that they visually recede and the highlights begin to "pop."
The second tip is to remember that high-contrast lighting can be your friend. Pretend you're an old-school film photographer shooting color transparency film: Expose for the highlights and let the shadows fall whether they may. Then think of the shadows as solid shapes. If the shapes look interesting to you, there's a good chance they will look interesting to someone else.