Wild camels first originated in North America, and then, before the last Ice Age, they spread from North America to East Asia and then across to Central Asia and Iran and Arabia (and also south to South Americawhere they became llamas and vicunas and alpacas). Then camels became extinct in North America, maybe during the Ice Age, but they survived in Asia and Africa.
People in Central Asia were the first people to domesticate (tame) camels. They tamed camels long after they learned to tame cows and pigs, maybe about the same time as horses (about 3000 BC). Like horses, camels are not as tame and stupid as cows and sheep are.
Camels can travel long distances across the desert without needing water, so they were very useful in the Gobi Desert in Asia and in the Persians, the Greeks, and the Romans used donkeys more than camels even in the desert. (For instance, when Jesus entered Jerusalem, he rode on a donkey). But around the beginning of the Islamic empire, maybe about 500 AD, somebody in West Asia invented a good pack saddle for camels. After that, people began to use camels as pack animals more and more.
Around the same time, people in India also began to use camels more, along with the Islamic invasions of India.
And people in China also began to use camel saddles. This statuette (small statue) of a man riding a camel is from the T’ang Dynasty China, about 800-900 AD.
Bibliography and further reading about camels:
Camels, by John Wexo (1999). Easy reading.
The Camel and the Wheel, by Richard Bulliet (1975). Bulliet lays out some reasons why camels became more popular around the time that the Islamic Empire was strongest – mainly the invention of a better camel saddle.