Good summary here:
The biggest problems we face in considering such a mission are:
How can we accelerate any probe to the speeds necessary (10% of the speed of light, per article)?
How can we build a probe to work properly during such a long voyage?
How can we power a probe for such a long voyage?
How can a probe send back the necessary information once it arrives?
Any such probe will have to have very little mass and also be able to make many decisions (AI) for itself to come close to achieving a successful mission. I am glad they are in the early stages of planning now. A lot of technological innovations will have to occur before this particular mission becomes anything more than a pipe dream.