In 2+1 dimensions quantum particles can exist that are neither bosons nor fermions. Such particles, known as "anyons" have been studied theoretically for over forty years. While there has long been good reason to believe that these particles exist, particularly in fractional quantum Hall systems, it has been frustratingly difficult to perform experiments that probe the properties of these particles --- with many failures over the year. However, just in the last few years, with the maturation of a few new technologies, there have now been several very different but increasingly clear experiments that directly measure the exotic exchange statistics of these particles. I will explain the history of some of these experiments, what they have achieved, and what remains to be done.