Linking the human brain to a computer, is it possible?

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Ok. I know everybody saw the movie Matrix but I haven't really :)) but I had an idea these last days. Can a computer be linked in some way to the nervous system of a human? The human brain functions on electrical impulses similar to what we have in PC's would there be a way to capture those and maybe figure out what each of the impulses control and do and maybe reverse the process, not only read the signals send some to the brain and trigger reflexes with it. To put it in an example, capture what your skin sends your brain when it feels cold, block that sense and send it the feeling that it's warm outside. This example would probably damage the body itself because it wouldn't trigger shivering and you would get a cold but you wouldn't feel it or it could be used for blocking pain. Probably people out there are studying this, but it shouldn't be that hard or is it? Take it to the next level and the brain could be tricked into believing that it's somewhere else, you could create a complex signal that shows the brain an image. I think this is what the film Matrix was about. So what do you think?