Research shows that babies usually spend the first part of the night in deeper sleep, and the second part in much lighter sleep. So its quite normal for babies to wake up every sleep cycle during the second part of the night, often from 2 or 3 am onwards (note: a babies' sleep cycle is around 45 mins vs. 90 mins for adults). During these lighter phases of sleep there is much more blood-flow to the brain, which some baby sleep experts say is actually positive for development and nerve growth etc. Doesn't feel so positive for mama though at 3am, then 4am, then 5am!
So its up to every mama to decide whether to let this natural situation be, and pass on its own, or whether to implement some form of sleep training. I guess that mostly depends on circumstances and mama's sleep needs, especially if she is working.
I found the lack of sleep in the wee hours a bit distressing in the early weeks, but I didn't feel comfortable with trying any sleep training. So we then happily and cosily popped our little guy in bed with us. He still wakes in the wee hours but only very briefly, he just checks we are there, might have a quick feed, then back to sleep. We all get much more sleep this way! Co-sleeping (when done as per the safety guidelines) also reduces the risk of SIDS, this helped me to relax at night as I wasn't worrying about him.
http://nd.edu/~jmckenn1/lab/
Good luck with whatever road you choose, and take comfort in the fact that when you're awake in the wee hours looking up at the moon, so many other mother's are looking up at the same moon too..
