Silicon nitride (Si3N4) is an advantageous material due its unique combination of mechanical, thermal, chemical, and electrical properties both at ambient and elevated temperatures. Because of these properties there are a wide range of applications for Si3N4 components. Applications include heat exchangers, environmental barrier coatings, osteointegration scaffolds, radomes, and integrated circuitry. Such applications often require geometric complexity for efficient and/or effective operation. However, traditional ceramics processing methods such as hot-pressing or die extrusion are typically limited to simple axis-symmetric shapes. With the advent of additive manufacturing, there has been significant advancement into the forming of geometrically complex Si3N4 components. This review documents additive manufacturing advancements that have demonstrated, or are capable of, fabricating Si3N4 components with complex geometry.