1. Of a liquid, to spill by flowing out of a container or over some barrier. You're going to need a bigger pot, or else that soup will spill over. The floodwaters spilled over the levee.

2. To go beyond the borders or parameters of something and into something else, especially due to growing in size or scope. It's hard to contain violence to just one neighborhood, you know. It's only a matter of time until it spills over into our part of town too.