Every kid is different...I know a lot of moms whose kids are 4 right now (the same age as my daughter) who still have them in pull-ups at night because otherwise they will wet the bed. My cousin's daughter was in some kind of pull-up/diaper at night until she was 6 (turns out she didn't empty her bladder completely when she peed, even though she felt she had) and for some kids it may be older than that.
My daughter did not potty-train until she was 3 years 8 months but then not only was she day-time trained in 3 days (for pee - poop took a while longer) but she has never had accidents overnight either. I still put a pull-up on her at night for the first month or so but it was always dry in the morning (and usually her diapers had been dry in the morning too, even prior to potty-training). Seems she has freakishly good bladder control for a 4 year old, because she can drink a bunch of water right before bed, get up in the morning, drink a couple cups of juice, and still have it be an hour before she actually has to go pee. She drinks plenty of fluids but can often still go several hours, or all day sometimes, without having to pee. My friend's daughter, on the other hand, can't go 30 minutes without having to pee - her mom is the same way and she thinks it may be because they have really small bladders, so their capacity is less.
I think it's a mistake to refer to it as "night-time training" because it's not necessarily something you can "train" a child in. There is a hormone in our bodies that naturally causes us to concentrate our urine more at night so we are not having to get up all the time to pee, but young kids are not making much of this hormone so they can't always really help that fact that they need to pee during the night and can't control it. It just has to happen on its own. Every child is different as far as when this hormone starts to kick in, which is why some kids still need some kind of pull-up or absorbent underwear until up to age 8.