I have converted my license a couple of times now and it is pretty easy. There is no ICAO license that I know of, yet, just licences that are acceptable to ICAO, which includes of course the FAA ticket.
Both the Saudi and Bahraini conversions required that I sit the AIP (law) exam for each country. I then did a check ride in the type I was to fly. In New Zealand it was the same, I had to sit the law exam, but I also required a current ATPL with 1000 co-pilot or 500 command on a multi-crew aircraft, and it was to be on the license I was to convert, and that license had to be current. I had to use co-pilot time from ages ago as my command time was on a license that was not current (I ended up converting my Canadian ATPL). I did a co-validation for Panama but it was as a trainer/checker so it was just a ride with the DGCA inspector I was to deal with throughout the contract, and it had to be renewed every three months.
My buddy started flying in Botswana a couple years ago and he converted a bare canadian commercial to theirs (300 total time), and again, just a co-validation.
The JAA is a different story. To convert the ATPL you require a heap of large jet (not turboprop, something in the range of a B737 as a minimum I think)command, I think the number is 1000, plus a total time minimum. Otherwise, it is sitting all the ATPL exams, 7 or 8 I think.
There you go. It's lots of fun and normally pretty decent pay and conditions as long as you are ever so slightly choosy with who you work for. Good luck with it.