Since I'm in California, I'll answer for my state:
Current California Law:
Children under 2 years of age shall ride in a rear-facing car seat unless the child weighs 40 or more pounds OR is 40 or more inches tall. The child shall be secured in a manner that complies with the height and weight limits specified by the manufacturer of the car seat. (California Vehicle Code Section 27360.)
Children under the age of 8 must be secured in a car seat or booster seat in the back seat.
Children who are 8 years of age OR have reached 4’9” in height may be secured by a booster seat, but at a minimum must be secured by a safety belt. (California Vehicle Code Section 27363.)
Passengers who are 16 years of age and over are subject to California's Mandatory Seat Belt law.
When can a child graduate to a booster seat?
California law does not address graduation time from a five point harness to a booster seat. In the interest of safety, do not rush to move a child into a booster seat before they’re ready. Each time you “graduate” your child to the next seat, there’s a reduction in the level of protection for your child. Keep your child in each stage for as long as possible.
A child is ready for a booster seat when they have outgrown the weight or height limit of their forward-facing harnesses, which is typically between 40 and 65 pounds. Read the forward-facing car seat’s owner’s manual to determine height and weight limits, and keep your child in a harnessed seat for as long as possible.
Children at this stage are not yet ready for adult safety belts and should use belt-positioning booster seats until they are at least 4’9″ and between 8 and 12 years old. Safety belts are designed for 165-pound male adults, so it’s no wonder that research shows poorly fitting adult belts can injure children