The anatomical features of human organs inherent in 3D medical images provide essential information for diagnosis, pre-treatment planning, and surgical guidance. However, the image quality, dimensions, and field of view of medical images can be restricted by the physical or hardware limitations of the imaging devices available during treatment. Medical image synthesis is a research field with a wide range of potential applications in radiology and computer-assisted surgery, and is of growing interest in a variety of medical imaging modalities. This paper reviews recent studies on medical image synthesis and statistical reconstruction of anatomical information not included in original images, specifically focusing on the two topics: 1) recovery of pixels missing due to image artifacts, and 2) higher-dimensional image reconstruction or so called 2D-to-3D (2D/3D) techniques.