You used to hear about chunks of blue sewage falling off airplanes and crashing through roofs or even hitting someone on the ground. That doesn’t happen much anymore, because airlines use a more modern system, although I can imagine some of the older planes haven’t caught up yet. Here’s how it works, from the folks at Smithsonian.
Bless Lothar and all the folks who do the dirty work that enable us to live in a civilized manner. By the way, when they mention “long haul flights” in which you get two meals, they are talking about international flights. You can fly from one end of the US to the other and not get a meal these days, but few people bemoan the lack of airline food. -via Bits and Pieces
As for "doing one's business" in-air, I have done so a few times, the last was a four hour flight to Japan. It may be the in-flight meal didn't agree with my stomach.