A wealthy donor or corporation gives — with no limit — to a 501(c)(4) "social welfare" nonprofit, which is not required to disclose its donors. That nonprofit then donates to a super PAC. The super PAC dutifully reports where it got the money: from the nonprofit. But the original donor's name never appears anywhere. Watchdogs call this "dead-end disclosure." When they want to bury it deeper, operators chain nonprofits together — one (c)(4) giving to another giving to another, "Russian nesting dolls" — or route it through shell LLCs formed for the sole purpose of hiding the source. The super PAC lists the LLC; the LLC leads nowhere.
The elected official knows exactly who funded the ads that put them in office. The voter does not — so no one can connect a policy favor back to the donor who bought it. Roughly a billion dollars in fully untraceable money has flowed through these channels since 2010.
Cross-reference a nonprofit's IRS 990 (grants out) against super PAC FEC filings (money in) to bridge the gap. 990s lag by a year+, so this is slow, backward-looking detective work.