Compliicated is something that is hard to explain. Example: Her relationship with her boyfriend is complicated.
Complex is something that has many factors going into the problem or situation. Example: Global warming is very complex so scientists have a hard problem finding a solution it.
Sophisticated is what you would use to describe something that is developed to high level. Example: This piece of technology is very sophisticated, only trained workers are allowed to use it.
There are more than just the meanings that I listed to these words. I tried to give you a general meaning or the one that I believe is the most common. :)