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The honest answer is that it's a grey area, and it depends partly on where you live. In May 2018, the US Supreme Court struck down the Professional and Amateur Sports Protection Act (PASPA) in Murphy v. NCAA. That ended the federal ban that had confined full single-game sports betting mostly to Nevada. Since then, each state has decided for itself. Most states have legalized some form of sports betting, through retail locations, online apps or both. Each one licenses online bookmakers through its own gaming commission or lottery, such as the New Jersey Division of Gaming Enforcement or the Pennsylvania Gaming Control Board. Several large states, including California and Texas, had no legal online sportsbook at the time of writing, and some states still prohibit sports betting entirely. Check your state's gaming regulator for its current status.
Offshore sportsbooks sit outside that system. None of them is licensed by a US state, which means none is authorized to serve customers in any specific state, even though they accept US players. Accepting American bettors and being authorized to serve them are two very different things.
At the federal level, two laws come up most often. The Wire Act of 1961 targets people in the business of betting or wagering who use wire communications to take bets across state or national lines. The Unlawful Internet Gambling Enforcement Act of 2006 (UIGEA) targets payments: it bars gambling businesses from knowingly accepting funds for unlawful internet gambling and pushes banks and processors to block those transactions. Both laws are aimed at online betting sites and financial intermediaries rather than individual bettors. That's why card declines are common and why crypto has become central to offshore online gambling. Federal authorities have prosecuted offshore sportsbooks in the past.
State law is a separate matter. A few states have statutes that can technically apply to individuals who gamble online with unlicensed online sportsbooks, though enforcement against individual bettors has been rare. Rarely enforced isn't the same as legal. Offshore sportsbooks let bettors in states without regulation, or with restrictions, place wagers, but that access carries legal uncertainty and offers no state protection. This is general information, not legal advice. If your situation calls for certainty, consult a qualified legal professional.