New parents seem to sweat the small stuff more than seasoned parents. And while it's true that babies develop at different rates, depending on when they were born, their temperament and myriad other factors, there are a few milestones that parents should look for as they enjoy watching baby grow. That grin you see on your 2-month-old's face might be gas, as his grandparents may like to say, but it also could be that your baby is registering happiness and showing it in that toothless grin. Around 8 weeks is when babies differentiate the emotion of being happy - when you're around - and being unhappy. It's about this time - from 2 to 3 months old - when babies begin attempting to roll over during tummy time (which should always be supervised). He might push up onto forearms, and this motion just might send him rolling - which can be startling for him at first! Grasping objects comes next at about 4 months, then the fun stuff like hugging and playing peek-a-boo begins at 5 months.