The Kakeya conjecture is one of the most famous and well studied open problems in geometric
measure theory. In this talk I will discuss the history of the problem, including the best results
to date. I will then go on to discuss some recent work in collaboration with Eric Olson (Reno,
Nevada) and James Robinson (University of Warwick). We introduce a technique we call 'cut
and move' which allows us to give very simple proofs of some dimension estimates for Kakeya
sets and a good heuristic for why the full conjecture should be true.