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Artificial intelligence (AI) as an emerging technology is gaining momentum in medical imaging. Recently, deep learning-based AI techniques have been actively investigated in medical imaging, and its potential applications range from data acquisition and image reconstruction to image analysis and understanding. In this review, we focus on the use of deep learning in image reconstruction for advanced medical imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and positron emission tomography (PET). Particularly, recent deep learning-based methods for image reconstruction will be emphasized, in accordance with their methodology designs and performances in handling volumetric imaging data. It is expected that this review can help relevant researchers understand how to adapt AI for medical imaging and which advantages can be achieved with the assistance of AI.