I recently gave a journal club talk at the CMX Journal Club about quasicrystals, which happily gave me cover to finally research what the heck they are. Previously, I had a lot of trouble getting my head around the oft-repeated mantra that quasicrystals have long range order, but no translational symmetry. What exactly does this mean, and how is it possible? How do we square it with the fact that quasicrystals can have discrete rotational symmetries?. The answer turns out to be that all these pieces fit together nicely in Fourier space. This viewpoint clarifies and unifies these concepts and helps explain some of the other strange properties of quasicrystals to boot.