Baby development at 3-4 months: what’s happening
Your baby is busy learning about emotions and communication. She’s starting to link what you say to your facial expressions. She loves your face, but she might find new faces really interesting too. She also knows your voice and can turn her head to you when she hears you.
Your baby is starting to show more emotion and might laugh out loud, smile when he sees and hears things he likes, and say things like ‘ah-goo’. He might even try talking to you in coos and sounds. When you talk he’ll listen, and try to reply. And when he’s alone, you might hear him trying to talk.
Any extra crying and fussing usually settles around 12-16 weeks.
Reaching out to grab things – like rings or rattles – or putting things in her mouth are some of the ways your baby learns about the world around her. She’ll love playing with objects and might also take a long look at them and shake them.
And now that your baby is using his hands more, he might stare at them in wonder and amazement. Sometimes your baby might cross his eyes when he’s looking at things – this is normal in the first few months.
When you hold your baby or help her to sit up, you might notice she has better control of her head movements and needs less support.
Around this age, your baby loves to move and will probably start rolling from tummy to back. When you give him tummy time, he might lift his head high or push up on his hands. He might even sit up with some support behind and on each side of his body.
Source: http://raisingchildren.net.au/articles/baby_development_4_months.html

