Travelers holding a valid U.S. visa can enter Puerto Rico freely—no additional visa, no separate application, no passport stamp. As an unincorporated U.S. territory, Puerto Rico shares the same immigration regime as the 50 states.
If you enter the U.S. under the Visa Waiver Program (ESTA), the same 90-day limit applies to Puerto Rico. Time spent in Puerto Rico counts toward your 90-day VWP maximum.
A U.S. visa doesn't authorize travel to other Caribbean nations (Dominican Republic, British Virgin Islands, etc.)—each has its own entry requirements. Puerto Rico is domestic; its neighbors are foreign.
Carry your passport and visa (or ESTA printout) when traveling to/from Puerto Rico. While immigration checks are rare on domestic flights, CBP conducts random inspections, and you'll need documents for hotel check-in, car rental, or ferry to Vieques/Culebra.