This article is a review of the material extrusion-based ceramic additive manufacturing (MECAM) processes. The discussion begins with details of extrusion with filament and paste, covering the most popular variants of paste extrusion-based MECAM techniques that can be differentiated based on paste type and the method of shape retention of the deposited layer: extrusion freeforming, robocasting ceramic on-demand extrusion, and freeze-form extrusion fabrication. The article then focuses on post-processing considerations and the mechanical properties of sintered ceramic parts. It concludes with information on innovation opportunities in ceramic additive manufacturing, such as incorporating UV-curing and gelation in the process and producing geometrically complex structures from shapeable green bodies.