When you retire abroad and you have just pension or Social Security income, your tax liability will not change because there's nothing that the US government offers you as a retiree that allows exempting retirement income from taxation. Your US taxes will be basically the same as if you were living in the US if your only source of income is retirement or pension income.
However, if you are working abroad, whether you are working for a company abroad or working for yourself, there are ways to eliminate or dramatically lower your tax burden because the IRS allows you a couple of different options on the tax return itself.
One is something called the Foreign Earned Income Exclusion whereby approximately US $100,000 worth of foreign earned income could be excluded from your tax return. Let's say you make $100,000 working for some foreign or US company and you're physically working abroad. The $100,000 shows up on your tax return as a wage, while a minus $100,000 would appear further down on that tax return to wipe it out so that you basically have no tax liability.
There are certain tests that you must qualify for to be able to utilize the Foreign Earned Income Exclusion. For most expats who are permanently living abroad, qualifying is quite easy.
There are people who live abroad in higher tax jurisdictions where the effective tax rate that they are paying in that country is higher than it would be in the US. Even in Third World countries like Peru, for example, if you're making a modest income, you're paying more taxes in Peru than you would in the US. In this case, the preferred way to avoid or eliminate tax on the US tax return would be to utilize foreign tax credits.
The reason I say that the foreign tax credit is preferable in this situation is that it could potentially wipe away all US taxes because every dollar paid in foreign taxes is offset in the US. If you have foreign tax credits left over, which means you paid more taxes locally than you would have in the US, these get carried over.
The same expat who then moves from a high tax jurisdiction to a lower tax jurisdiction country, could use his or her carry over tax credits in a place where he or she would be paying less taxes than in the US. These carry over credits could be bankable.
Another reason why foreign tax credits are great for people who have children is that the child tax credit was eliminated a couple of years ago when one utilizes the Foreign Earned Income Exclusion on the tax return. Now, if you're using the foreign tax credit to eliminate your tax liability and you've got two kids under the age of 17, you could potentially get $2,000 in tax refund from the IRS without having paid any taxes to the IRS. This is why utilizing foreign tax credits can be the preferred way of taking care of your US tax return.
If you're using the Foreign Earned Income Exclusion and you qualify via either one of the two tests, it is possible to still pay no taxes in the country in which you are making the money if that country utilizes what's called a territorial tax system or has a zero tax rate. There are many countries in the world that have a zero tax rate or a territorial tax system. One example of a country with a territorial tax system is Panama.
If you are a US tax payer working in Panama and/or making money in Panama, it could be possible that you make $100,000 in Panama, utilize the Foreign Earned Income Exclusion to exclude out that $100,000 from the US tax return, and pay Panama zero taxes.
There are many expats who have local businesses or work for a local company and they pay taxes. There are people who work online and they are off the radar screen. If you're off the radar screen in a foreign country and you're not paying any taxes locally, you would not utilize the foreign tax credit because you haven't paid any taxes. You would clearly use the Foreign Earned Income Exclusion.
The tax situation mentioned in Panama as an example, I would bucket this more generally as a situation wherein if you are not paying taxes locally, then clearly the Foreign Earned Income Exclusion would be the preferred method.
For those with dual citizenship who have businesses in the country that they're in and paying local taxes that are higher than what they would pay in the US, it would be better to utilize the foreign tax credits.
(The beach town of Mazunte, near Oaxaca,Mexico, pictured.)
In the state of Quintana Roo (includes Cancun, Cozumel, Playa del Carmen, Tulum, and here in Akumal, the best beaches are in Tulum. Tulum’s beaches have crystal clear waters and sand that is like powder. Tulum’s beaches are amazing. For kilometers, you’ll only see the white sand and the crystal-clear water. 
The number one reason people should not retire to Panama is if they come with the attitude that it will be just like America. They should stay at home if they feel that way because they can’t be happy if they can’t adjust to the different pace of the lifestyle here in Panama, to the fact that not all stores have American products, that some things are not that convenient. We learned to deal with inconvenience in all walks of life and in all countries. It is different here. So...
Actually it’s a bit of a joke when you put on airs because it’s very relaxed here. The formalities are more authentic about families and being the person you are. 
Portugal has cut down quite a lot of holidays. Portugal is a Catholic country that had a tremendous amount of holidays for saints that they’ve had to cut down on. 
There is no surfing in Ambergris Caye because the ocean is not that rough, which I think is very nice because that way you can swim in the ocean and you don’t have to worry about the rip tides or the waves crashing down at you or getting washed out to sea. There is, however, wind surfing now here on Ambergris Caye because it gets pretty windy around the island, but there is no wave surfing here. 
Driving south on Highway 1 from after it intersects Highway 5 is fairly uneventful, if by “uneventful” you mean "the hundreds of times when you’re confronted with the fact that even a slight miscalculation on your steering wheel will result in certain death." A half inch to the left, and you’ll crash head-on into a semi barreling towards you at 60 miles per hour. A half inch to the right, and you’ll go over the roughly 12-inch shoulder to plunge either into...
These places would seem to the native inhabitants to be neglected lands of unruly bushes and trees with views that were pretty, but where one did not linger while on one’s way to somewhere else. But to Mike Cobb, these were places to turn into communities with a network of pathways close to the cool porches of neighbors one would regularly visit.