The strong embodied mind thesis holds that the particular details of one's embodiment shape the phenomenological and cognitive nature of one's mind. On the face of it, this is an attractive thesis. Yet strong embodiment faces a number of challenges. In particular, there are three prominent misconceptions about the scope and nature of strong embodiment: 1) that it violates the supposed multiple realizability of mentality; 2) that it cannot accommodate mental representation; and 3) that it is inconsistent with the extended mind thesis according to which mentality extends, not only beyond brain, but beyond body as well. In this paper, we seek to dispel these three misconceptions by explaining what strong embodiment does and does not entail.