It has been in the news lately. How big a problem is it? Not very. The total number of jobs exported is estimated (very approximately) at 200,000 per year. By comparison, the total number of job losses from all sources (including quits) is about 4,000,000 per month. Source: Economagic. This is offset by about the same number of hires per month. This means that outsourcing is responsible for less than 1% of all job losses.
There is another side to this: automation. Take my field (computer programming) as an example. Originally (back in the 1940s) engineers hard wired computers to solve problems. Then John von Neumann pointed out that since computers process information, and instructions are information, computers could process instructions. So, he proposed the stored program concept. Later, others replaced machine language (binary zeros and ones) with assembly language. (Von Neumann thought that using computers for such "clerical" was a waste of valuable computing time.) Assembly language allowed the programmers to use mnemonics instead of binary codes. Later, programmers noticed that they were using sets of code repeatedly, so they added a feature so that a set of code could be defined, then used with a single command. This is called Macro Assembly Language.
Next, higher level languages like FORTRAN and COBOL (third generation languages) were developed. That further simplified writing programs. After that, programmers noticed that certain tasks (e.g. compressing data) were being done many times, so they wrote utilities to do them. Most recently, Object Oriented Programming was developed. It is sort of a way to automate the writing of utilities. The main lesson of this is that if you find yourself doing something over and over, then you shouldn't be doing it.
The programming jobs that are being outsourced to India are those that can be specified precisely in a contract. But those are the jobs that can be automated. So, with some exceptions, the jobs that are being outsourced overseas are the ones that are only a step or two away from being automated out of existence.