President Kennedy signed Proclamation 3447 in February 1962, embargoing trade with Cuba. The Cuban Assets Control Regulations followed in 1963 and remain the operative instrument, administered by the Office of Foreign Assets Control at the US Treasury.
What it did to the industry
Growers and makers displaced after 1959 rebuilt where they could — Nicaragua, Honduras, the Dominican Republic — carrying seed, technique and in several cases brand names with them. The result is that many historic marcas now exist in two entirely separate versions, a Cuban one and a non-Cuban one, made by different companies from different tobacco, sharing nothing but the name. An American reader meeting a famous brand is very often not meeting the Cuban product at all.
Whether a traveller may bring them back
This has changed more than once. Personal importation was permitted under rules introduced in 2016 and then withdrawn in 2020. Because it is set by regulation rather than statute, it can change again, and the current OFAC guidance is the only reliable answer at any given moment.
What it is not
It is not a customs classification of quality, a health measure, or a statement about the cigars. Confusion on this point is old and persistent, and the scarcity the embargo created has done more for the reputation of Cuban cigars inside the United States than any campaign could have.