I'm wondering why mutual fund should have the geographical limitations? Many US funds are not tradable outside US, Others outside Europe. Why? And from where do these limitations come? Is there any US mutual fund which is tradable in emerging market (say Ukraine)?

I don't know that American funds won't happily take your money, regardless of who you are and where you live. However, if you are talking abotu ETFs, then those don't trade elsewhere because it costs money to list and there perhaps isn't enough interest to justify it.

The issue is trading, not ownership. Public mutual funds in the US are public securities, and public must be marketed according to strict Securities and Exchange Commission and Internal Revenue Service rules.As a practical matter, many people buy these from outside the US by obtaining a US address (that of a friend or family member who will forward mail) and US taxpayer ID number (just file a form). Another popular approach is to open a brokerage account with a US address.Richer people open offshore accounts (accounts in places that do not have much financial regulation) for the same purpose.In addition to satisfying the US laws, you would have to consider the laws of your residence jurisdiction.