The flag of the Red Crescent is what happened when the world's first universal humanitarian symbol turned out not to be universal. A red crescent on a white field, it does precisely the same legal work as the red cross: hold fire, medics here. But where the red cross was designed at a conference table in Geneva, the crescent was improvised in wartime by an empire that refused to fight under a cross, and it took international law fifty years to catch up with the fact.
An objection from the Ottoman ranks
The Ottoman Empire was an early adopter of the Geneva system. It acceded to the 1864 Geneva Convention in 1865, and an Ottoman aid society for wounded soldiers was founded in 1868, only a few years after the events at Solferino that started the whole movement (told in full in this site's Red Cross entry). The trouble was the emblem itself. To Ottoman commanders, a red cross on white did not read as neutral Swiss geometry. It read as a crusader's cross.
The break came during the Russo-Turkish War of 1876-1878. The Ottoman government informed Switzerland, the depositary state of the Geneva Convention, that the red cross was offensive to Muslim soldiers and that its own medical services would fly a red crescent on a white ground instead, an inversion of the Ottoman flag's white crescent on red. The note came with a promise, though: Ottoman forces would continue to respect the red cross protecting Russian medics. It was a unilateral move, made in the middle of a war, with no basis in the treaty text. The ICRC accepted it for the duration of the conflict, and in 1878 conceded that it should in principle be possible to adopt an additional protective emblem for non-Christian countries.
Fifty years of limbo
Nothing in the Geneva Convention was actually changed for half a century. The crescent existed on sufferance: used by Ottoman forces, tolerated by other belligerents, absent from the law. Egypt took it up as well, and Persia introduced a third emblem of its own, the red lion and sun.
The Diplomatic Conference of 1929, convened to revise the Geneva Convention after the First World War, finally regularized the situation. At the request of the Turkish, Persian and Egyptian delegations, and after long argument about whether multiplying emblems would wreck the system's simplicity, the conference recognized the red crescent and the red lion and sun as distinctive emblems with equal standing to the cross. The concession came with a lock on the door: to stop further proliferation, recognition was limited to the countries already using those emblems.
The lock did not quite hold. The 1949 Geneva Conventions, drafted after the Second World War, kept the crescent and the lion and sun in Article 38 of the First Convention but rejected every proposal for new emblems, including Israel's red shield of David, a refusal that stayed unresolved until the red crystal was created in 2005 (that story has its own entry). Iran abandoned the lion and sun in 1980 after the revolution, switching to the crescent, so of the three emblems recognized in 1929, two remain in active use.
Who flies it today
More than 30 of the movement's national societies use the crescent, nearly all of them in Muslim-majority countries. Turkey's society, the Kızılay, is the direct descendant of the Ottoman aid society and one of the largest humanitarian organizations in its region. Egypt followed early. Others arrived by conversion: Pakistan switched its society from cross to crescent in 1974, Malaysia in 1975, Bangladesh in 1989, each change requiring legislation, since the emblem a country uses is fixed in domestic law.
The movement's own name eventually caught up. In 1986 the International Conference adopted the name International Red Cross and Red Crescent Movement, and the federation of national societies is now the International Federation of Red Cross and Red Crescent Societies. On joint operations the two emblems fly side by side, and the ICRC's count as of the mid-2020s is roughly 150 societies under the cross and over 30 under the crescent.
A crescent without a rulebook
The Geneva Conventions are strict about what the emblem means and silent about what it looks like. No shade of red is specified, no proportions, not even which way the crescent should face. Most societies draw it with the horns opening toward the fly, but mirrored versions appear, and Turkey's crescent is noticeably slimmer than Egypt's. The white field and the red crescent are the whole of the legal requirement.
The protection, by contrast, is exact. The crescent enjoys the same status as the cross under the 1949 Conventions and the same protection in domestic law: unauthorized commercial use is an offense in most countries, and using the emblem as cover for military action is perfidy, a war crime. On hospital roofs in Gaza, on ambulances in Istanbul, on relief convoys after earthquakes in Pakistan and Afghanistan, the crescent is the region's standing instruction not to shoot. Whether a second emblem strengthened the system by making it acceptable to more of the world, or weakened it by breaking the rule of one universal sign, is an argument the movement has been having since 1876. The thirty-odd societies flying the crescent suggest the first answer has at least worked in practice.
References
[1] ICRC, "History of the emblems." https://www.icrc.org/en/article/history-emblems
[2] "Emblems of the International Red Cross and Red Crescent Movement," Wikipedia. https://en.wikipedia.org/wiki/Emblems_of_the_International_Red_Cross_and_Red_Crescent_Movement
[3] Geneva Convention for the Amelioration of the Condition of the Wounded and Sick in Armies in the Field, 1929, Article 19; First Geneva Convention, 1949, Article 38.
[4] "Turkish Red Crescent," Wikipedia. https://en.wikipedia.org/wiki/Turkish_Red_Crescent
[5] François Bugnion, Towards a Comprehensive Solution to the Question of the Emblem (ICRC, 2000).