Three-dimensional (3D) printing is a highly automated platform that facilitates material deposition in a layer-by-layer approach to fabricate pre-defined 3D complex structures on demand. It is a highly promising technique for the fabrication of personalized medical devices or even patient-specific tissue constructs. Each type of 3D printing technique has its unique advantages and limitations, and the selection of a suitable 3D printing technique is highly dependent on its intended application. In this review paper, we present and highlight some of the critical processes (printing parameters, build orientation, build location, and support structures), material (batch-to-batch consistency, recycling, protein adsorption, biocompatibility, and degradation properties), and regulatory considerations (sterility and mechanical properties) for 3D printing of personalized medical devices. The goal of this review paper is to provide the readers with a good understanding of the various key considerations (process, material, and regulatory) in 3D printing, which are critical for the fabrication of improved patient-specific 3D printed medical devices and tissue constructs.