Some of these are very good and do not cause significant problems for 56k, while others cause major problems for 56k and sometimes for other modem protocols. All the usual things that degrade phone service and hinder normal modems connections will interfere with 56k modems also. Many of these degradations are introduced by users themselves. See our page on connections problems for info on how to avoid causing your own problems. This robustness in the presence of audible noise and interference is all the more remarkable given the sensitivity of 56k to other much more subtle effects.
Trunks use a wide range of different digital technologies, so they come in many kinds.
Regardless of how they are implemented, they are divided into two classes. The signals carrying the calls are processed differently for the two kinds of trunks. The difference is very slight but has a big effect on 56k calls. Calls switched onto trunks that can carry long distance calls have no digital pad, while those on local-only trunks do get a digital pad. The digital phone service ISPs use to provide 56k dialup is delivered to them on what are essentially trunks.