Several of my relatives have brought fine carved teak and rosewood furniture and Kashmiri carpets over from India (we are Indian). The big stores will handle shipping since they deal with a lot of foreign buyers. Shipping and handling fees can be high if going though the store, but they generally do a good job of packing.
Customs is not an issue as long as the proper paperwork is filed. No one had a problem with damage. That can be a headache even with insurance.

^ We had an antique desk shipped across the US and it came broken. You have to pay the big bucks if you want to make sure things are shipped carefully.

Funny Question. I have friends who bought a nice teak dining set while visiting relatives in India. Cost to ship to Baltimore was less than 200. Cost from Baltimore to the DC area was a couple thousand (costs add up when you have to get mover and a truck, even if the truck is mostly empty). Also, one of the dining table legs was cracked in shipment and they spent years trying to find a carpenter to make a replacement.

Interesting idea. Am from India but never considered this? Is it cheaper? Better quality?

There is nice furniture made in America. Just saying.

Anyone buy furniture from another country? How is the process of shipping, customs, etc