Epiphysis and articular surface are always used for bone age assessment in hand radiographs, and they can also provide reliable references for radiologists to diagnose bone-age-related diseases. However, it is difficult to obtain the accurate epiphysis and articular surface from hand radiograph due to the following problems: 1) overlapping epiphyses cause blurred boundaries and 2) the epiphysis varies greatly and its morphology is irregular. To address such issues, an adaptive region-aware attention network (ARAA-Net) is proposed for epiphysis and articular surface segmentation, where the adaptive channel region-aware attention (ACRAA) module, which can capture the channel details of feature maps, is designed to discriminate the overlapping boundaries of epiphysis regions; then, the adaptive spatial region-aware attention (ASRAA) module, which can learn the spatial distribution dependence of feature maps, is devised to obtain the bone morphological information. Experiments conducted on the Tailored Hand Radiograph Subset of Radiological Society of North America (THRS-RSNA) dataset show that the proposed ARAA-Net outperforms the state-of-the-art deep-learning-based methods and further assists radiologists to perform bone age assessment. The project is available at https://github.com/langdecc511/ARAA-Net.