"for the king's ships kept going to Tarshish with Hiram's servants, and once every three years the ships of Tarshish would arrive bearing gold, silver, ivory, apes, and peacocks"
The Bible, Chronicles II
China is the sole nation on earth where giant pandas are found naturally, and the Chinese government controls the supply of pandas found in zoos around the world. The government provides pandas to zoos in other nations - sometimes as gifts, more often on loan - for reasons that have as much to do with politics and publicity (probably more so) than with research and conservation.
The most famous exchange, of course, was that which followed US President Richard Nixon's visit to China in 1972. Besides opening up relations with the communist state, Nixon received Hsing-Hsing and Ling-Ling, the giant pandas who came to live at the National Zoo in Washington, DC. The Chinese, in turn, received musk-oxen. How musk-oxen were chosen over eagles, bison, and a host of other emblematic American species is beyond me...
Hsing-Hsing and Ling-Ling were not the first exotic animal ambassadors to make their appearance on the world stage. Zoos have existed for thousands of years, often in the form of royal menageries, and across those millennia kings, queens, pharaohs, and other rulers have exchanged animals with one another. References to the practice can even be found in the Bible ("... camels bearing ivory, apes, and peafowl"). Sometimes these exchanges have been straight up trades as rulers sought to bolster their own collections; the Holy Roman Emperor Frederick II traded his giraffe for the Caliph of Egypt's polar bear. Some were gifts, such as the lions that became the nexus of the Tower of London menagerie. Some were even ransoms; when Richard the Lionhearted was captured following the Crusades, part of his ransom was two white gyrfalcons, the most prized of falconry birds.
Few animals had (almost) the impact on world history and politics, however, as an Indian rhinoceros that found itself in Lisbon, Portugal in 1515.
The rhinoceros itself had been a gift to the Portuguese from the Sultan of Cambay in modern India. It was then sent on the long, perilous, and (one can only imagine) extremely uncomfortable voyage back to Europe via Africa. King Manuel of Portugal was himself a collector of beasts and tried to show off his new prize by staging a fight between the rhino and an elephant, based on the ancient belief that the two are bitter enemies. The fight never happened as the elephant fled in panic. With his gladiatorial ambitions thwarted, Manuel turned from pleasure to business.
At the time, Portugal was competing with Spain (the only other major seafaring power in Europe at the time) for papal grants to the newly discovered lands of the New World. Eager to curry favor, Manuel decided to gift his rhino to Pope Leo X. The animal was shipped to Rome, stopping along the way for an audience with the King Frances of France. Alas, Francis was to be the last monarch that the rhinoceros would meet. The ship sank of the coast of Italy and the rhino was drowned. The animal - and Manuel's hopes of using it to bribe the Pope and win his favor - were lost. How the world might have changed if it had reached Rome and delighted the Pope as the Portuguese had hoped can only be imagined. It may very well have changed the history of the world dramatically if Portugal, not Spain, had gone on to dominate the Americas. Then again, maybe not - perhaps the Spanish would have countered with some equally outlandish animal and re-won the Pope's favor.
Although the rhino died far from home, in a sense it did achieve a form of immortality. The beast was seen by many Europeans, and a description reached the famous German painter and printer Albrecht Durer. Durer executed a somewhat fanciful rendering of the animal, complete with armor plating and a horn on its shoulder, that for centuries became the standard image of the Indian rhinoceros.
It's uncertain as to whether Pope Leo X ever saw a copy of the engraving. If he did, it's all that he ever received of what was to be his rhinoceros.