I've been on the Summit, which is a bit larger than Century but I guess would have the same general atmosphere. During the day anything goes, but I found people to be generally respectful as far as covering up bikinis inside the ship (except a few teenagers). I found the dinners to be quite dressy and was very thankful I bought a black suit for my husband before we went. I wished I had brought at least one really fancy dress, like a black sequined sheath or something but I did ok with nice tea-length dresses and black hose with pumps. You'll see a lot of tuxes and gowns on formal nights, which look great but aren't necessary if you have a nice suit and dresses. Even the semi-formal nights were pretty dressy, and casual nights meant nice dockers with dress shirt; nice sundress or pantsuit for ladies. I never saw jeans or shorts in dining room- if someone doesn't want to dress up they can go to the other dining options on the ship.