We have placed a lot of emphasis on connections and interactions amongst different societies and civilizations. Consider the different ways in which these connections have occurred (trade, conquest, migration, for example); the cultural, economic, social, religious, and political changes they have spurred; and the varying reactions of people to inter-cultural contact. Don't forget to consider instances of isolation or separation (i.e., Mesoamerica vs. the rest of the world) as well as instances of connection and interaction.

The rise of Christianity as an offshoot of Judaism is an example of a culture spreading due to missionary activity. Judaism is not a missionary religion, and so remained isolated until Christianity (the subset of Jewish people who recognized Christ as a Messiah), which required missionary work, was adopted by the already powerful Roman Empire (formally sanctioned by the Emperor Constantine in 313).
The rise of Islam gained similar strength, but owing to trade (which was already common in Arabia for the unique incense and spices there) and military conquest. Muhammad, the founding prophet of Islam, died in 632 without naming a successor. Following his death, various sects of Muslims focused on spreading Islam by means of military conquest.
At about the same time as the beginning of Islam, Indian merchants traded with merchants in Southeast Asia, spreading Buddhism and Hinduism. In summary, sometimes the religions prescribe expansion (as in Christian missionary work or Islamic jihad, or “holy war”), and other times religions (and their attendant customs and general culture) follow trade.