In the software world, it's a mixed bag. You can offshore code to India and get back nice, usable code, or you can offshore code to India, or even China these days, and get back complete dogsh*t that you have to re-write. The former is cost-effective, the latter, of couse, is awful.
Basically, the best offshoring code shops are those set up by people who've spent some time in the US and understand the way we communicate and do things. Those guys then go home to their native countries, open up a code factory, and make out like bandits.
I did some (property tax) contract work for Citigroup several years back. They brought in about 100 "Southeast Asians" through an agency for a tech project that worked on the same floor.
Simply put, it was a bad fit culturally. I don't know about the women, but many of the men used the restroom sinks for bathing...I ultimately availed myself of the restrooms on different floors.
They're lovely people, but they can't drive to save their lives. They're hard workers, and their children increase the competition in our school district, which is fine by me. My 10 YO has set his sights on matriculating at UT-Austin...he'll have to finish in the top 8% of his class to qualify for admission. By the time he finishes HS, it may be top 5%.