Quantitative PET imaging requires an attenuation map to correct for attenuation. In stand-alone PET or PET/CT, the attenuation map is usually derived from a transmission scan or CT image, respectively. In PET/MR, these methods will most likely not be used. Therefore, attenuation correction has long been regarded as one of the major challenges in the development of PET/MR. In the past few years, much progress has been made in this field. In this review, the challenges faced in attenuation correction for PET/MR are discussed. Different methods have been proposed to overcome these challenges. An overview of the MR-based (template-based and voxel-based), transmission-based and emission-based methods and the results that have been obtained is provided. Although several methods show promising results, no single method fulfils all of the requirements for the ideal attenuation correction method for PET/MR. Therefore, more work is still necessary in this field. To allow implementation in routine clinical practice, extensive evaluation of the proposed methods is necessary to demonstrate robustness and automation.