Start with the Migration Overview page from World Bank for foundational context.
Go to Business Databases: A-Z and click on the Economist Intelligence Unit to search for remittance information for certain countries. Click on EconLit to search for articles on this topic. Another option would be to try OECD iLibrary.
For background information on remittances from the United States, see the Migration Information Source.
Also see the Global Remittances Guide from the Migration Policy Institute.
To find books on this topic, search under the subject "emigrant remittances" or "balance of payments" in BU Libraries Search.