Radiotherapy (RT) is one of the basic treatment modalities for cancer of the head and neck (H&N), which requires a precise spatial description of the target volumes and organs at risk (OARs) to deliver a highly conformal radiation dose to the tumor cells while sparing the healthy tissues. For this purpose, target volumes and OARs have to be delineated and segmented from medical images. As manual delineation is a tedious and time-consuming task subjected to intra/interobserver variability, computerized auto-segmentation has been developed as an alternative. The field of medical imaging and RT planning has experienced an increased interest in the past decade, with new emerging trends that shifted the field of H&N OAR auto-segmentation from atlas-based to deep learning-based approaches. In this review, we systematically analyzed 78 relevant publications on auto-segmentation of OARs in the H&N region from 2008 to date, and provided critical discussions and recommendations from various perspectives: image modality — both computed tomography and magnetic resonance image modalities are being exploited, but the potential of the latter should be explored more in the future; OAR — the spinal cord, brainstem, and major salivary glands are the most studied OARs, but additional experiments should be conducted for several less studied soft tissue structures; image database — several image databases with the corresponding ground truth are currently available for methodology evaluation, but should be augmented with data from multiple observers and multiple institutions; methodology — current methods have shifted from atlas-based to deep learning auto-segmentation, which is expected to become even more sophisticated; ground truth — delineation guidelines should be followed and participation of multiple experts from multiple institutions is recommended; performance metrics — the Dice coefficient as the standard volumetric overlap metrics should be accompanied with at least one distance metrics, and combined with clinical acceptability scores and risk assessments; segmentation performance — the best performing methods achieve clinically acceptable auto-segmentation for several OARs, however, the dosimetric impact should be also studied to provide clinically relevant endpoints for RT planning.