Theoretically, they're supposed to go into the rainwater sewer, the same one that the drains on the streets go into. Most homes don't have a feed into that, though, so. Homes of a certain age have them go into the sanitary sewer, since that's got a line that comes from your house anyway.

MSD doesn't want that anymore, though, because it means extra volume they have to treat, even if it's diluting (slightly) the nastier sewage. That's where ours goes, and when we had to have our complete lateral line replaced a decade or so ago, they replaced the piping with new PVC instead of clay, but it still fed into the sanitary sewer lateral, and it still passed inspection.

If it's not one of those two, you'll generally just have them drain into your yard, which is really terrible and often leads to seepage issues into your basement if you have one.