Project Icarus aims to answer these questions, and to re-evaluate the findings of the previous Project Daedalus, which took place in 1973-1978. Have we come any closer to being able to realize an interstellar probe? From the Project Icarus blog:
"Project Icarus is a theoretical design study with the aim of designing a credible interstellar probe that will serve as a concept design for a potential unmanned mission that could be launched before the end of the 21st century. Icarus will utilise fusion based engine technology which would accelerate the spacecraft to approximately 10% to 20% the speed of light."
So check out the Project Icarus blog, and subscribe, as I've already done.