The consumer point-and-shoot camera has just been reinvented—not tweaked, or remodeled, but actually re-thought from top to bottom. A Silicon Valley start-up called Lytro is shipping this week a camera that looks like no other and actually lets you focus or refocus your pictures on a computer after you take them.

Not only that, but the company is promising that pictures you take with the camera today will be able to be manipulated after the fact in additional ways in coming months. For instance, you'll be able to snap into...