The special rules of U.S. Taxation and the non-U.S. spouse

The above tweet references a post from Jane Bruno about the U.S. tax implications  of the “non-American spouse” which includes in part:

If you are married to a non-American and you both live overseas, you may have wondered how this impacts on your U.S. tax filing situation, if at all. As with most concerns involving taxes, the more complicated they can make it, the better Congress likes it! This article will try to present your various tax obligations (and options) with regard to a non-American spouse as simply and precisely as possible.

Read on! To be forewarned  is to be forearmed!