The additive manufacturing of bioceramic parts has been investigated since the 1980s. This paper offers an overview of the present achievements in the production of alumina, zirconia and hydroxyapatite parts by means of selective laser sintering/melting of a powder bed or stereolithography. A focus is placed on these specific materials because of their widespread use in the biomedical field. It demonstrates that even though the manufacturing of parts with these processes is possible from pure bioceramics, the use of a binder (or another chemical adjuvant) is required in order to achieve good mechanical properties. Still, improvements in the raw material preparation and in the comprehension of the physical phenomena occurring during the processing remain necessary to be able to prevent the formation of cracks or to be able to control the porosity of the parts.