In Britain the Royal Navy has a shortage of experience sailors essential to operating some of its warships. The need is most acute in technical fields. That is sailors with the skills and experience to make repairs at sea. The shortage arose because over the last few years the Royal Navy suffered such heavy budget cuts that they could not afford to new recruits needed to replace the experienced sailors retiring. So in an increasingly common move Britain asked the United States for help, offering to pay all costs and expenses to entice American sailors to serve on Royal Navy ships. The U.S. Coast Guard stepped up and found 36 sailors who had the qualifications and were willing to move to Britain with their families for a few years and serve on Type 23 frigates.
This sort of thing is nothing new, especially among English speaking countries. Back in 2010, noting that Britain was downsizing its armed forces, and cutting loose a lot of experienced personnel, the Australian Navy sent recruiting officers to Britain to see if there would be interest among some of these former (or soon-to-be former) British sailors in joining the Australian Navy. The Australians were particularly interested in obtaining personnel with technical skills. Years of low unemployment in Australia (partly because China was buying so many raw materials) caused a shortage of engineering and technical specialists in the navy. The mining companies were luring away a lot of technical personnel with higher pay and better working conditions. As a result, for example, the navy only has crews for three of its six submarines.
Australia has long been recruiting foreigners who possess needed technical skills and speak English. Australia is a nation of immigrants and the navy points out that recruiting a foreigner is cheaper than training an Australian to do these tasks. But sending recruiters to foreign countries was a new angle. Australia also offered navy jobs to sailors from Canada, New Zealand, and the United States. All four foreign nations share a common language and, in general, culture with Australia. Moreover, sailors from these foreign nations have gone through similar security vetting. The recruiting offers were sweetened with quick granting of Australian citizenship after less than a year of service.
Australia is not the only nation seeking foreigners for its military. Russia, for example, has a fundamental problem with few Russian men willing to join, even at good pay rates. Efforts to recruit women and foreigners have not made up for this. The Russian military has an image problem that just won't go away. This resulted in the period of service for conscripts being lowered to one year (from two) in 2008. That was partly to placate the growing number of parents who were encouraging, and assisting, their kids in avoiding military service.
Nevertheless, Russia kept making it easier for foreigners to join. Recruits still must be able to speak Russian, have no criminal record, and meet physical and educational standards but other than that, anyone is welcome to sign up for five years as a contract (non-conscript) soldier. This didn't bring in a lot of new people but every little bit helps. The navy and air force are particularly short of technically qualified personnel and don't care if the new guys speak with an accent. At its peak this program had less than a thousand foreigners serving, most from countries that used to be part of the Soviet Union. But there were also a few from Germany and Israel (where a lot of Russians had immigrated to in the past 30 years).
Before the U.S. military began downsizing in 2012 they had about 50,000 non-citizens in service (out of some 2.2 million active duty and reserve troops). The navy, not the army, usually has the largest number (nearly half). That's something of a navy tradition, as hiring foreigners to serve on U.S. warships is a custom that goes back over a century. Currently, the proportion of foreigners (about two percent) in the U.S. military is historically low. It's been much higher in the past, often reaching 25 percent or more. This caused alarm, then as now, but there were never a lot of problems with uncertain loyalties.
After 2001 senior American officers urged more efforts to recruit foreigners. Not just non-citizens with green cards but foreigners who were not residents of the United States. This brought forth protests from those opposed to, well, whatever. Historically, the American military has usually had more foreigners in the ranks than it does now. During the American Civil War about twenty percent of the Union Army was foreign born troops. There were entire divisions of Irish, Germans, or Scandinavians. For the rest of the 20th century, the all-volunteer military continued to have a higher (than today) percentage of foreigners. Recruiting foreigners would enable the army to get more highly capable recruits and ones with needed foreign language and cultural awareness skills. Naturally, they would have to speak acceptable English, just as resident foreigners in the United States or citizens from Puerto Rico must. While American military pay and benefits are competitive with U.S. civilian occupations to most foreigners these pay levels are astronomical. The risk is low, as only about one in a thousand foreign born volunteers died in Iraq or Afghanistan. All that and you get to become a citizen of the United States after your four year enlistment is up. The only question was which line would be longer at American embassies, the one for visas, or the one for military recruiting?
And then there is Britain. In the early 19th century Gurkhas were first recruited into the British Indian army, not the British army. After India became independent in 1947 they too recruited Gurkhas for Indian infantry units. But service in the British army was considered a better deal. Britain has long recruited foreigners into its army and navy because there has always been a shortage of British citizens willing to serve.
Then there is the French Foreign Legion, which is supposed to be nothing but foreigners (except for the officers). But many French join, claiming to be from the French speaking parts of Belgium. No matter, if otherwise qualified, the "Belgians" are signed up. In Italy, the Vatican (a small part of Rome that is an independent country controlled by the Roman Catholic Church) gets most of its security forces from Catholic areas of Switzerland. This is the Swiss Guard. While the French Foreign Legion dates from the 19th century, Swiss have been serving as foreign mercenaries since the 15th century. But these contingents disappeared as better economic opportunities developed in Switzerland and mercenaries became less popular.