Attenuation correction (AC) is essential for the generation of artifact-free and quantitaAtively accurate positron emission tomography (PET) images. PET AC based on computed tomography (CT) frequently results in artifacts in attenuationcorrected PET images, and these artifacts mainly originate from CT artifacts and PET-CT mismatches. The AC in PET combined with a magnetic resonance imaging (MRI) scanner (PET/MRI) is more complex than PET/CT, given that MR images do not provide direct information on high energy photon attenuation. Deep learning (DL)-based methods for the improvement of PET AC have received significant research attention as alternatives to conventional AC methods. Many DL studies were focused on the transformation of MR images into synthetic pseudo-CT or attenuation maps. Alternative approaches that are not dependent on the anatomical images (CT or MRI) can overcome the limitations related to current CT-and MRI-based ACs and allow for more accurate PET quantification in stand-alone PET scanners for the realization of low radiation doses. In this article, a review is presented on the limitations of the PET AC in current dual-modality PET/CT and PET/MRI scanners, in addition to the current status and progress of DL-based approaches, for the realization of improved performance of PET AC.