Quoting the Wikipedia as a quick reference, long-exposure photography or time-exposure photography involves using a long-duration shutter speed to sharply capture the stationary elements of images while blurring, smearing, or obscuring the moving elements. When a scene includes both stationary and moving subjects (for example, a fixed street and moving cars or a camera within a car showing a fixed dashboard and moving scenery), a slow shutter speed can cause interesting effects, such as light trails. Long exposures are easiest to accomplish in low-light conditions, but can be done in brighter light using neutral density filters or specially designed cameras.

Leaving your camera in a stationary position (on a tripod, for instance) with the shutter open for a relatively long interval can produce some very nice and unexpected effects. I’ve tried it myself sometimes, for periods as long as 30 minutes, to make some experiments while shooting at night. 

But how about leaving the shutter open for years? That’s what Michael Wesely has been doing for a while. This post on Petapixel.com, Photographs Captured Over Years with an Open Camera Shutter shows some examples. 

Michael Zhang writes:

In the mid-1990s, [Wesely] began using the technique to document urban development over time, capturing years of building projects in single frames. In 1997, he focused his cameras on the rebuilding of Potsdamer Platz in Berlin, and in 2001 he began photographing the Museum of Modern Art’s ambitious renovation project. He uses filters and extremely small apertures to reduce the amount of light striking the film, creating unique images that capture both space and time.

The results are breathtaking. The caption of the image I’ve chosen to repost here says: 9.8.2001 — 7.6.2004 — The Museum of Modern Art, New York. You can find more in his book, Open Shutter, available on Amazon. (I’m sure it was also available on the MoMA Store, but I can’t find it at the moment.)