One of the problems that you could face quite often is a clogged drain line.
When you have a clog, the water will not be able to drain from the sink or the shower stall, and eventually, it will start to back up into the basin. It can also cause a rather unpleasant aroma.
Another one of the problems with your drains might simply be age, and they might need to be replaced. Structural damage caused by tree roots, and even accidents can cause issues as well. In those cases, a repair could be possible, but more than likely, part of the drain system will need to be replaced.