Mine just started a loose routine in the past 2 weeks (she just turned 3 months this past Sunday). For DD, it just means that she doesn't fight it as much and her naps are longer.
At 2 months we had a great routine, at 3 months it went out the window. She became a terrible napper! A couple weeks ago she started taking one long afternoon nap so I'm rolling with that, though out of nowhere she took a morning one today. That hasn't happened in a month or so.
With my ds I can count on 3 regular naps...but the lenght isn't consistent. He's 4 months. My dd started regularly sleeping well during the day at 9 months.
Re: When do babies start
DD started around 3 months.
Now that doesn't mean she's completely regular every day. She still isn't. But most days she is.