When will my baby start sleeping through the night?

Depends on luck. Most babies will sleep through the night at age 6 weeks to 6 months.
It varies. As one can imagine, babies have different internal rhythms just as we adults do. Having said that, the average baby can sleep 9-12 hours at a time at night by 9 months old. Ways to encourage healthy sleep patterns include developing a nighttime routine (which can include a warm bath, reading or singing to baby), and allowing babies to fall asleep in their own crib while still partially awake.