Now that you've passed the initial stage of parenthood, which simply involves adjusting to life with a newborn and all that it entails, you're still probably running on a sleep deficit and buried in diapers, but hopefully ready to sit back and enjoy your baby's blossoming personality and his ability to better explore and interact with you and the world around him.
MILESTONES A word on milestones: Now that your baby is becoming more visibly skilled at mastering new developmental tasks, it is (and will continue to be) important for you to keep in mind that every child is different and that milestones only serve as a rough estimate. Your baby may be early on some, and late on others. Quite simply, milestones give parents (and doctors) a way to assess whether children are developing as expected. After all, we know, in general, the "average" age at which the "average" child will be able to accomplish all of the skills involved in growing up — everything from smiling and cooing to rolling, sitting, talking, toilet training, and learning to tie shoes. If at any time you have concerns or if your baby doesn't do things such as develop better head control, focus on and follow objects, bring his hands to his mouth, or coo and giggle when talked to by the end of the first few months of life, be sure to discuss it with your baby's doctor.
In general, infants between 1 and 3 months old: Begin to coo and gurgle. Instead of simply being startled by sounds, babies start to respond more specifically to sounds — first by turning their heads and changing their facial expressions, and then by actually cooing and gurgling. These sounds will probably be music to your ears, as well they should be. You can consider these sounds to be your child's first words to you, as simple cooing and other verbalizations represent the very beginning of language development.
Develop better head control. While all three-month-olds still need special attention paid to supporting their heads, they definitely require less support than as a newborn. Don't let your infant's increasing head control fool you, however — many three-month-olds like to show off their abilities while being held, only to suddenly thrust themselves back, causing their heads to flop over.
Track sights and sounds. While healthy newborns can both see and hear, by the time they reach three months of age they tend to actually follow objects with their eyes, and purposefully turn their heads to locate sounds.
Have better control of their hands. Along with better head control, infants gradually develop the ability to hold objects in their hands (instead of just grasping things reflexively) as well as to bring their hands to their mouths.
Start to show signs of mobility. Between two and three months, infants typically go from raising their heads and chests when lying on their stomachs to being able to push themselves up fully on their forearms. If you haven't witnessed the result already, be aware that this is the precursor to rolling over. While the standard age that infants begin to roll is closer to 4-6 months, quite a few two- or three-month-olds have excelled in this eagerly anticipated milestone.