Human pose estimation, the process of identifying joint positions in a person's body from images or videos, represents a widely utilized technology across diverse fields, including healthcare. One such healthcare application involves in-bed pose estimation, where the body pose of an individual lying under a blanket is analyzed. This task, for instance, can be used to monitor a person's sleep behavior and detect symptoms early for potential disease diagnosis in homes and hospitals. Several studies have utilized unimodal and multimodal methods to estimate in-bed human poses. The unimodal studies generally employ RGB images, whereas the multimodal studies use modalities including RGB, long-wavelength infrared, pressure map, and depth map. Multimodal studies have the advantage of using modalities in addition to RGB that might capture information useful to cope with occlusions. Moreover, some multimodal studies exclude RGB and, this way, better suit privacy preservation. To expedite advancements in this domain, we conduct a review of existing datasets and approaches. Our objectives are to show the limitations of the previous studies, current challenges, and provide insights for future works on the in-bed human pose estimation field.