Where the water should go
Away from the house, and not into the sewer. Belleville’s wastewater department says a downspout that disappears into the ground is probably connected to the sanitary sewer, calls that an illegal connection, and wants roof water sent to the yard or a storm sewer instead. University of Illinois Extension gives the plain version: keep downspouts clear and make sure they drain away from the home.
A buried line does that out of sight. Each one is laid out from the gutter layout, the grading, the soil and the amount of runoff, with the pipe sized and sloped to a discharge point that will not send the water back toward the foundation or onto a neighbor.
Old drains that stopped working
We also repair existing downspout drains. Leaves and grit pack them, roots crush them, and some were routed into the sewer decades ago. A strip of soggy yard along the house, like the one in the photo here, is often the first sign.

