The United States made it illegal for citizens to travel to Cuba in 1962, following the Cuban Missile Crisis. This ban extended until 1977, when President Carter chose not to renew it. In 1982, President Reagan made it illegal to spend money in Cuba, effectively reinstating the ban on travel.
The original ban on travel in 1962 was initiated in an effort to tighten the embargo on the island nation, with the goal of forcing Fidel Castro from power. After President Kennedy's death in 1963, his brother Robert Kennedy argued for lifting the ban, but the Johnson administration ruled this out. The formal travel ban lasted for 14 years before lapsing, and in 1979, President Carter allowed Americans to visit their family members in Cuba.
The Reagan administration quickly took a hostile stance toward Cuba, and while the new restrictions did not explicitly forbid travel to Cuba, they banned Americans from giving money to Cubans outside of a set of very narrow circumstances. Those who spent money in Cuba without authorization could face stiff fines and penalties. The Bush administration changed these rules to allow up to $100 of spending per day, but bringing back certain goods from Cuba was still illegal due to the embargo, especially cigars.
In 1999, President Clinton relaxed many of the restrictions, allowing more chartered flights to Cuba and increasing the spending allowance to $185 per day. In 2000, private person-to-person chartered tours became available, which expanded over the next decade. In 2014, President Obama announced his intentions to further ease travel restrictions with the goal of finally normalizing relations between the United States and Cuba.