In recent years, free-flight shows have become increasingly popular in zoos and aquariums; at some facilities, especially bird-centric ones, such as the National Aviary, they are the star attraction. I still remember the first time I attended one, during my first visit to the San Diego Wild Animal Park years and years ago. The flights are a testament to the new zoo philosophy of allowing animals to express as much natural behavior as possible, both for the welfare of the animal and the education of the visitor.
The training that goes into them, however, is far older than the shows... older, possibly, then the zoos themselves. Free flight shows find their origins in an ancient sport that was one of one mankind's earliest efforts at animal husbandry... one that is still practiced today, including by some zookeepers that I know. The sport is falconry.
Falconry describes the use of trained bird of prey of hunt wild game. It may vary from a kestrel taking small birds and rodents to a golden eagle bringing down a grey wolf, a feat still accomplished in some parts of Central Asia. The practice is believed to have originated in the Middle East over 4000 years ago, spreading throughout Europe and Asia. Over the centuries, it transitioned from a means of securing prey in the arid grasslands of Mesopotamia to the sport of kings and emperors, with one's social status in part defined by what bird one flew. A truly spectacular bird, like a pure white gyrfalcon, was worth far more than its weight in gold. The subject was so important that a personage no less than the ruler of the Holy Roman Empire, Frederick II, took it upon himself to write a textbook on the subject.
Now, the captive breeding of birds of prey didn't occur until considerably later in history, so for most of the history of falconry, birds were taken from the wild. The advantage of this was that the bird presumably already knew how to hunt. The disadvantage was that it was a wild bird which had no desire to have any sort of association with humans. The birds had to be taught to obey the commands of their human handlers and, most importantly, to come back. Training techniques that were used with a dog or horse wouldn't work on a hawk or falcon. A hunter couldn't beat a hawk, or force his will upon it. If he did, then the bird would simply fly off the moment it was released for a hunt, never to return. The bird had to want to cooperate. Falconry may have been responsible for the earliest development of training with positive reinforcement.
As firearms became more prevalent in the 1700s, falconry began to decline in popularity, though it never died out completely. This, it turns out, was a blessing for birds - many of the husbandry techniques developed and passed down by falconers over the years ended up playing a crucial role in the conservation of endangered birds of prey in the mid-and-late twentieth century, including one of the most iconic of falconry species, the peregrine falcon.
Today, falconry is perhaps one of the most heavily regulated sports on earth. New falconers must apprentice themselves to masters for years, develop facilities for their birds, and acquire permits. All of this to obtain a hunting partner which may still opt to abandon you forever the first time you take the field together. Ensuring it doesn't do so requires lots of patience, lots of training, and lots of trust. One former zookeeper roommate of mine took up falconry. His relationship with his red-tailed hawk was so close that they'd often eat dinner at the table together... I stayed at the other end. (Come to think of it, I seem to remember seeing him with that hawk a lot more than I ever recall seeing him with his girlfriend).
Eagles and other raptorial birds, while majestic, are inclined to laziness in a zoo setting, and even with the largest of aviaries, they can be difficult to encourage to fly and exercise without sufficient reward. The skills of falconry leant themselves to the establishment of free-flight shows in zoos and aquariums... minus the part where the bird kills something at the end.