thank you! do you just mean the usual bath vent fan? we have a window but it is rarely opened since it faces the street.

I have wallpaper in my bathrooms and there are no issues.

I have an excellent vent fan which runs when it senses the moisture in the room is above a certain level. I don't have condensation on my mirrors and any condensation on my shower walls is dissipated almost immediately. I guess if one has a bathroom like a steam room with inadequate ventilation and one keeps the door closed all the time, there might be issues :-).

thanks Helen, that sounds ideal! do you happen to know the model of your bath fan?

Wallpaper's fine. We have it in one bath (installed by me) and 15 years later, no problems. And I still really like it; it suits this house.

My fan is a Panasonic Whisper fan. I think there are different models depending on square footage of the room.

When we finally took the wallpaper off the bathroom walls in 2014, just to update, not because of a problem, we found that we'd written the date we pasted it up written on the wall: 1984! That bathroom didn't have a fan either until we put one in in 2014. It did have a window. We put in a Panasonic Whisper Green. Great product!

sounds like wallpaper is fine and the panasonic fans are the way to go. thanks everyone!

You could always do hand painted stripes and It becomes a non issue

Since wallpaper isn't an issue in a bathroom, what is the aesthetic or functional point of limiting oneself to painted stripes?

The reason people select wallpaper is there is a universe of design choices that are then possible.