Historically, most women have given birth long before age 35. To do so at 35 or later was indeed quite rare. Society has begun moving in a new direction, though. In this day and age, about 20% of women have what are known as 'geriatric pregnancies'.
Reasons for the changes can be chalked up to changing attitudes about women, for one; women have more freedom to pursue various paths as opposed to a rigid set of expectations. They are also making more use of contraceptives which are easier to get and are now less of a taboo.
Some complications do arise if women wait too long to decide to have children. Not only does fertility decrease with age, but treatments become less effective. Consider a 30-year-old. If she has a 20% chance of becoming pregnant each month, it's only about 5% by the time she reaches 40.
Older mothers run a higher risk of experiencing setbacks for themselves and their babies, partially because of the age of the mother's eggs. Miscarriages, chromosomal abnormalities, and a higher risk for Down's syndrome have all been noted. It's recommended that women have children in their prime childbearing years to have the greatest chance of a successful pregnancy.

