Functionally graded materials (FGMs) are multifunctional materials, which display a quantitatively controlled gradual spatial variation in composition and/or microstructural parameters, in order to control variations in structural or functional properties and so improve properties of the final component with respect to a homogeneous material. Here we will focus on FGM in which one of the materials/phases is a ceramic compound. Emphasis will be on the processing methods that have been used for the processing of ceramic composites. Initially, most of the processes for FGM production were based on a variation of conventional manufacturing methods. Later on, around 2010, additive manufacturing (AM) methods have been explored and this has given the research field of FGM a new boost. 
Conventional manufacturing methods can be broadly classified into two fields: bulk processing methods  and coating methods. For the fabrication of bulk FGMs, powder processing is most economic and suitable for mass production.  Among the different colloidal processing techniques, electrophoretic deposition (EPD) has been successful because it is a fairly rapid, low-cost process for the fabrication of ceramic coatings as well as bulk materials. Functionally graded materials varying in thickness from a few nanometers to centimeters are possible. Some examples for different applications will be shown.
Additive manufacturing (AM), often also called 3D printing, is a range of processes whereby parts are built by adding material, usually layer by layer directly from a computer-generated 3D model. It can be considered as a near net shape manufacturing process, which can directly manufacture complicated 3D objects without requiring molds, tooling or the need for joining or assembling. Many AM techniques can be adapted to produce FGM components with complex geometry and gradients. Since ceramics are commonly fabricated from powders we will limit the presentation here to AM methods using powders.
In the direct energy deposition process (DED) focused thermal energy is used to fuse powders fed into the laser focus, allowing the direct fabrication of ceramic-ceramic and metal-ceramic composites. However, DED has some significant limitations because high thermal gradients and extremely fast cooling rates invariably result in the development of thermal stresses, often leading to delamination and cracking. Powder bed fusion (PBF) as well as other powder bed-based AM techniques have not been so successful for the processing of FGM. More successful have been ceramic extrusion techniques, for which several variants have been reported. Important advantages of these are their relative ease of operation as well as the low costs since a high-energy beam is not involved. Their success relies on the precise control of the rheological properties of the extruded paste or filament. Continued development of equipment and technologies has made it possible to produce a material with nonlinear gradients in 1D, 2D, and 3D. Another promising technique is direct inkjet printing (DIP) also called material jetting. By the use of multiple printheads, DIP has the unique advantage over all other AM technologies in the ability to deposit droplets of multiple materials simultaneously. This enables in fact microstructure tailoring on a voxel-level.