Background
The various classical civilizations established vast trading networks with one another.  The exchange of goods and ideas occurred from the time of the early Indian Empire on the Indus River, all the way up to the Roman Empire on the Mediterranean. In some cases, this exchange was very one sided, but remain mutually beneficial despite this.

Phoenician Trade
The Phoenicians were an early trading civilization located in present day Lebanon and Syria along the Mediterranean.  They produced various products, such as glass, papyrus scrolls, and dyes, and established trade across the entire Mediterranean Sea. The Phoenician trade empire benefited most cultures in this region.  As their trade expanded, they setup colonies throughout the Mediterranean.  The Phoenicians also developed an alphabet to keep track of their business dealings.  This alphabet was later adopted and adapted by the Greeks and Romans, and is the basis for the western alphabets of today.  Phoenician trade is responsible for the great exchange of ideas and culture that occurred during this time period.

India
Trade had occurred between India and the Middle East since the first people settled along the Indus River.  After Alexander the Great conquered part of India in the 4th century BCE, he established a permanent trade route between India and the Mediterranean.  By the 2nd Century BCE, vast amounts of goods traveled from India into this region, such as textiles, gems, and various spices.  This contributed to the new Hellenistic culture, which was a blending of Greek, Persian, Egyptian, and Indian ways of life.  New trade routes were established both overland into central Asia and China, and across the seas into the Middle East, Egypt, East Africa, and Southeast Asia.  This exchange resulted in a vast sharing of knowledge, goods, and culture.
 

The Silk Road
The Han Dynasty established a trade route known as the Silk Road. This trade route reached as far as Mesopotamia, and was a main conduit for the exchange of goods and ideas between China and other civilizations.  Over time the trade route reached 4,000 miles.  Most merchants never traveled the entire route, but instead traded their goods at one of the many markets established along the way. China's main export for many centuries was silk, while in return they imported such goods as, glass, muslin, and various food products like cucumbers and grapes. Many cultures depended on this trade route for goods and services.

China - Korea - Japan
Under the Tang Dynasty of China, Korea became a tribute state.  They adopted many Chinese beliefs and practices such as Confucianism and the civil service exam.  Because Korea was in near constant contact with Japan, many of these ideas were passed on to them.  This is known as the Korean Bridge between China and Japan.  Later, Japan would make direct contact with China and establish a system of trade of both goods and ideas.

Roman Empire
Extensive trade occurred throughout the Roman Empire during the Pax Romana.  Products such as, Egyptian grain, African ivory and gold, and Indian cotton and spices moved freely across the empire.  The Roman Empire also traded with the Chinese through the use of the Silk Road.  Lots of cultural diffusion took place during this period, as various cultures came to depend on each other for the exchange of goods and ideas.
 

Trade throughout the Roman Empire