President Obama's historic moves to restore diplomatic relations with Cuba are raising new questions about how U.S. citizens can travel to Cuba, and perhaps most importantly for many, whether it's now legal to buy Cuba's famed cigars.

But despite Obama's efforts, Americans still face real limitations in the law in terms of how they can trade with, and travel to, the communist island. Below is a quick checklist of what you can and can't do.

What about those cigars?

People who are experts in the art of rolling up tobacco leaves into cigars say the quality of Cuban cigars has waned over the years, but many still long for the stogies that have been prohibited in the U.S. for so long.

Under rule changes announced by Obama in January 2015, American traveling to Cuba for authorized reasons are allowed to buy personal consumption goods while they're visiting. And now, people will be allowed to bring up to $400 worth of goods bought in Cuba for personal use.

"This includes no more than $100 of alcohol or tobacco products," the government said in January.

But it's still illegal to buy Cuban tobacco or alcohol from third countries or over the Internet. That means your dream of jumping across the border to Canada to pick up Cuban products there and bring them back to the U.S. legally remains a dream.

Can I travel to Cuba now?

Under Obama's rule change, traveling to Cuba is now easier than it's been in decades, but it still doesn't mean you can plan a vacation trip to the island.

Travel restrictions that were initially imposed by executive order decades ago were codified in the Helms-Burton law of 1996. And to fully eliminate those travel restrictions, Congress will have to change the law.

Under current law, there are 12 categories of authorized travel, including family visits, official government business, journalism, education, religious activities, athletic competitions and other public performances, support for the Cuban people, and humanitarian reasons.

Over the years, some of those categories have required "specific licenses," which essentially means the government must pre-approve the trip. Others have only required "general licenses," which means people traveling for those approved reasons can go, and check in with the government later on their trip.

What Obama did in January is to make all of these travel categories subject to "general licenses," making it much easier for people to go.

If you can go to Cuba, you'll be allowed to buy what you want for personal consumption while there, and Obama's rule change will let you use credit and debit cards.

But again, note that "family vacation" or "honeymoon" are not approved categories for travel.

How does the embargo play into all of this?

Along with the travel rules, the embargo against Cuba was codified in 1996, and it will take a change to the law to lift it. Obama is hoping to convince Congress to do just that, but Republicans seem highly unlikely to oblige him.

Republicans in general have said Obama is giving too much away to Cuba, and should be demanding democratic reforms and the release of political prisoners. So the embargo seems likely to hang around for a while longer.

But the embargo is not a monolith. For example, the Treasury Department's Office of Foreign Assets Control is able to license certain transactions between companies, and has done so over the years.

Trade in food and medicine has been going on for years now, under the Trade Sanctions Reform and Export Enhancement Act of 2000, and Obama's rule changes in January were aimed at making that trade even easier.

Obama also took steps to allow companies to set up telecommunications links between the U.S. and Cuba, and allow banks to maintain correspondent accounts at Cuban banks to help process authorized transactions.

Do we have normalized relations now?

The U.S. and Cuba have agreed to re-establish embassies in their respective countries, after more than 50 years. Before that, each country maintained an unofficial embassy of sorts in the other nation, called an Interests Section.

As of July 20, under an agreement between President Obama and Cuban President Raul Castro, those Interests Sections will become embassies.

But it may still be a while before the U.S. installs a Senate-approved ambassador in Cuba, since Republicans and even many Democrats oppose Obama's gestures toward Cuba and may have luck in blocking a new ambassador to Cuba.