Ponzi schemes are fraudulent investment schemes that promise high returns by using money from new investors to pay earlier backers, ultimately collapsing when new investment stops. Historical examples include Charles Ponzi's Securities Exchange Company in the 1920s and Bernie Madoff's scheme in 2008, which defrauded investors of $64.8 billion. Warning signs include promises of high returns with little risk, emphasis on recruiting new investors, and lack of transparency about operations.