In the 1960s and 70s many engines used timing chains, but because of vibration and noise issues, many manufacturers began using rubber belts.
The positive aspect of belts is that they are smooth and quiet and the disadvantage is they periodically need to be replaced. The mileage interval for replacing most belts is from 60,000-105,000 miles. Because timing belts are made of rubber compounds, age also causes them to get dry and cracked. If a vehicle is not driven very many miles, timing belt replacement should be done at a 6-7 year interval.
Today, due to design improvements chains are becoming quieter and smoother and therefore we are beginning to see more new models using chains which in theory last the life of the engine.