Over the first year or two of your baby’s life, her eyesight goes through a journey from a point where she can only see around 8 to 12 inches from her face (and even then only in black and white) to a point where she can see as clearly as any adult can, and has the hand-eye coordination to go with it.
The transformation doesn’t happen in your baby’s eyes, though - her eyes are fully equipped to see the world when she is born. In fact, your baby's eyes are already about 65 to 70% of their full size. Imagine if your baby’s feet were only going to grow about 30% more! The part of your baby that needs to grow so she can perceive the world around her isn’t her eyes, but her brain. Technically, your baby’s eyes can work just as well as yours, but she just can’t process that visual information yet. For instance, when your baby is first born, she has a much lower ability to perceive light than an adult, which helps her sleep even in environments you would think would be too bright for her, at least until she is a little older, and her improving eyesight turns her a little fussier. Even with this limited sight, though, babies can distinguish their primary caregivers' faces from the faces of other adults after just a few hours of close contact with them
During the first months of life, the eyes start working together and vision rapidly improves. Hand-eye coordination begins to develop as your baby starts tracking moving objects with her eyes, and then reaching for them. By 8 weeks, babies are able to more easily focus their eyes on the people nearest to them.
your baby’s light perception and nearsightedness don't start to approach the way an adult sees until she is around 3 months old. Colors are another story, though - your baby only sees in black and white for a few days, but by the end of her first week, she is already starting to see warm colors - generally red first, followed by yellow, orange and green. Blue and purple take a little longer to develop. At first, she can really only see bright colors and high contrasts, which could be why pastels have fallen out of fashion in baby toys - they may look adorable, but your baby won't be able to see the colors in them well enough to know that until she’s a little older, though no less adorable herself.
In your baby’s first 3 months, you might notice her eyes start to wander, sometimes without being synchronized with each other, as your baby is still working on getting both eyes to work together. She might also look kind of cross-eyed. If one of her eyes seems to always wander in one direction, there’s a chance that it could be a sign of a problem, so you might want to mention it to your baby’s healthcare provider, but generally, it’s perfectly normal, and should slow or stop by the time your baby is around 3 months old.
By the time your baby is around 3 months old, she is starting to lose her nearsightedness, and her light-perception is a lot closer to what it’ll be like when she is fully grown. She should also be able to follow moving objects with her eyes, and be able to switch her focus from one object to another without moving her head not long after that. your baby should begin to follow moving objects with her eyes and reach for things around 3 months old.
When your baby is around 4 months old, she will start to be able to tell different people apart based on the internal structures of faces, like eyes, nose, and mouth, instead of just by face shape and hair, which were her best visual cues for faces until that point. Now she won’t ever have to wonder again if she's meeting a different person just because they’ve gotten a haircut!
Until she is around 5 months old, she doesn’t have much in terms of depth perception, but around 5 months, that sense starts to kick in, which helps her out with tasks like reaching for and grabbing objects, and throwing them. By around her fifth or sixth month, her sense of color is almost fully developed, though she still probably has a preference for bright colors and strong contrasts. This increased visual awareness can feed into the development of stranger anxiety, or a fear of people your baby hasn't met before, or does not see regularly.
The next significant milestone for your baby’s eyesight comes whenever she starts crawling, because crawling helps her work on strengthening the connection between what she can see and what she can do with her body - her hand-eye coordination, yes, but also its lesser-known cousins, foot-eye coordination and limb-eye coordination, and general spatial awareness. Her coordination and depth perception also get good enough around 9 months that she can throw things with more precision - just what every parent has been waiting for.
From there, your baby is pretty much just honing and sharpening her visual and perceptual abilities, until some time, usually between her first or second birthday, when she has vision that can measure up to pretty much any adult’s.