We sleep-trained our first starting at about 6 months old, and we're about to do the same with our second. The strategy we used was some kind of incremental back-off. Put them down, light out, leave. Wait 5 mins. Go on, give them a little hug or back pat, leave. Wait 10. Then 15. Then 20. Then 30. Then stay at 30 until they fall asleep.

Next night, 10, 15, 20, 30, 30, 30...

next night, 15, 20, 30, 30, 30....

At some point it went up to like 30 mins for first check, then an hour for subsequent checks. I think if we'd gotten to that point we'd consider trying something else cause that's a lot of crying.

But in practice we never had to really adhere to most of the structure because iirc it was like:

Night 1: 5, 10, 15, asleep. Night 2: 10, 15, asleep. Night 3: asleep. Night 4: 15, asleep.

Then he was sleep trained and has slept like a rock with 0-30 seconds of fussing (usually 0) (and ~never crying) since.

This is called the Ferber method and it worked very well for us as well. Note to others considering using it, the method is just as much about the ritual leading up to sleep (bath, reading a book, etc)

“Solve your child’s sleep problems” by Richard Ferber, M.D. is the book which includes this. It also includes a lot more, including an overview of sleep physiology including phases, as well as lots more like details about night terrors and other “partial arousals”.

The big thing he says for going to sleep is to set up the desired sleep associations (eg, alone in the crib in a dark quiet room if that’s what you choose) and then ensure the child falls asleep in that situation and it doesn’t change while they sleep. So for instance, don’t let them fall asleep on your lap then move them to the crib, because when the next normal sleep cycle ends and they partially wake up, they will discover something is different and get upset.

Ah I can see that, we've always had a pretty rigorously-respected bedtime routine.

The baby is crying because they want attachment to the parent. Give them the love they want. Don't deprive them of love by letting them cry it out. Comfort them!

You're not wrong. But at the same time... it's a very effective method with some babies. One thing often missing from these discussions is the practicality. Yes, responding to your child like that would be ideal. But it just can't be done if they literally just cry constantly when put to bed. And some babies do that! Sleep-deprived parents who come to actively resent their child's crying is a very real thing. And probably far worse for development and attachment.