Formal breast development begins at thelarche, which starts in half of women at around 8 years old. Breast tissue actually can develop at several points throughout the life cycle. You can actually have premature breast development as a newborn from residual estrogen from the mother. This usually resolves around 2 years of age.
Classically, breast development from puberty "ends" around 16-21 years of age. However, women in menopause can sometimes develop additional breast tissue. This is usually adipose tissue ("fatty" breast development) but is often a reason that women seek breast reduction/ and/or removal of breast implants.