I've heard that babies can have a wakeful period at around four months, where a baby who's been sleeping fine all of a sudden starts waking during the night. Why does this happen, and how should I deal with it?

Like Hui Qun mentioned, your baby is probably going through sleep regression. What I did was to lessen his activities an hour before his nap time, and to ensure he has at 3 naps during the day so that it's easier to get him to sleep. Also, I have a flask of warm water & canisters of measured milk powder so that I can make the milk as soon as possible if he wakes up for milk. I am a light sleeper and he co-sleeps with him, so I usually wake up at his slightest movements. By the time I'm done making his milk, I can dreamfeed him and *most* of the time, he continues sleeping. Otherwise, I let him sleep on me and that seems to help calm down a lot.