In current combined PET/MR systems, PET attenuation correction is based on MRI, since the small bore inside MRI systems and the strong magnetic field do not permit a rotating PET transmission source or a CT device to be integrated. Unlike CT measurements in PET/CT scanners, the MR signal is not directly correlated to tissue density and thus cannot be converted by a simple transformation of intensity values. Various approaches have been developed based on templates, atlas information, direct segmentation of T1-weighted MR images, or segmentation of images from special MR sequences. The advantages and disadvantages of these approaches as well as additional challenges will be discussed in this review.