I'm not sure about overseas, but in the US, there are very specific and strict rules regarding the bird species you can keep and under what circumstances.
For example (now it may have changed since I looked into it), during an apprenticeship, you must work in the rescue/rehab/conservation aspect of raptors.
After achieving your apprecticeship falconry permit (after about a year), you are only eligible to obtain, handle and train a Red Tailed hawk.
It is not an easy, or cheap hobby, nor is it one that anyone but the most serious can do.
As for keeping them caged, the only caged raptors I know of in captivity are those unable to fend for themselves, and of course all are caged during roosting hours for safety.
Part of the art of falconry is training the birds to be free flying.