Owing to freedom of design, simplicity, and ability to handle complex structures, additive manufacturing (AM) or 3D printing of ceramics represents a promising enabling technology and has already been used to produce geometrically complex ceramic components and ceramic metamaterials. Consequently, novel applications for additively manufactured ceramics, which leverage their structural, high temperature, and chemical-resistant properties, have been proposed in areas ranging from electrical engineering and micro/nanoelectronics to chemical engineering to biology. Polymer derived ceramics (PDCs) represent a relatively new class of materials within additive manufacturing. PDCs enable the development of ceramic parts patterned via low-cost polymer 3D printing methods followed by pyrolysis in a high temperature process in which the polymer itself forms a ceramic often in the absence of any ceramic filler. PDCs have served as a feedstock for various 3D printing techniques for which a wide range of physiochemical factors can be tailored to optimize the ceramic manufacturing processes. In particular, the silicon and carbon-rich polymeric microstructure of PDCs offers a high degree of tunability and potential to achieve a closely defined combination of functional, thermomechanical, and chemical properties. In this review, we cover mechanisms underlying the design and manufacture of ceramics via 3D printing and pyrolysis of preceramic polymers, focusing on chemical formulations, printing technologies, and the mechanical performance of the ceramic network from microscale to scale. We also summarize experimental data from the literature and present qualitative and quantitative comparisons between different AM routes to provide a comprehensive review for 3D printing of PDCs and to highlight potential future research.