What are people buying when they give money away? Is pure altruism possible? Who benefits from grants to charities and subsidies to givers? Is religious giving different? Which fundraising approaches "work", and is more charity always better? Questions like these make philanthropy and fundraising among the most dynamic research areas in economics today. This research review guides students and scholars from the time when giving was seen as "irrational", to the present when economics has fully embraced the complex and fascinating challenges of understanding why self-interested people can be so unselfish.