Ceramic matrix materials have attracted great attention from researchers and industry due to their material properties. When used in engineering systems, and especially in aero-engine applications, they can result in reduced weight, higher temperature capability, and/or reduced cooling needs, each of which increases efficiency. This is where high-temperature ceramics have made considerable progress, and ceramic matrix composites (CMCs) are in the foreground. CMCs are classified into non-oxide and oxide-based ones. Both families have material types that have a high potential for use in high-temperature propulsion applications. The oxide materials discussed will focus on alumina and aluminosilicate/mullite base material families, whereas for non-oxides, carbon, silicon carbide, titanium carbide, and tungsten carbide CMC material families will be discussed and analyzed. Typical oxide-based ones are composed of an oxide fiber and oxide matrix (Ox-Ox). Some of the most common oxide subcategories are alumina, beryllia, ceria, and zirconia ceramics. On the other hand, the largest number of non-oxides are technical ceramics that are classified as inorganic, non-metallic materials. The most well-known non-oxide subcategories are carbides, borides, nitrides, and silicides. These matrix composites are used, for example, in combustion liners of gas turbine engines and exhaust nozzles. Until now, a thorough study on the available oxide and non-oxide-based CMCs for such applications has not been presented. This paper will focus on assessing a literature survey of the available oxide and non-oxide ceramic matrix composite materials in terms of mechanical and thermal properties, as well as the classification and fabrication methods of those CMCs. The available manufacturing and fabrication processes are reviewed and compared. Finally, the paper presents a research and development roadmap for increasing the maturity of these materials allowing for the wider adoption of aero-engine applications.