This article presents a general overview of ceramic matrix composites (CMCs) and their applications. General properties are presented and most common types of ceramic matrices and different reinforcements. High temperature in processing and service of CMC components require optimal matrix – reinforcement combinations that must consider their temperature resistance, chemical compatibility and thermal expansion mismatch. General insights into mechanisms that govern the crack deflection and arresting in CMCs are presented. Typical oxide and non-oxide CMCs are shortly described, whereas matrices made of alumina (Al2O3), zirconia (ZrO2) and silicon carbide (SiC) accounts for the major part of applied composites today. Aerospace applications have been the most influential drive of CMCs development and research, but applications of CMCs are very important in versatile areas where components operate in hostile high temperature environments, like heat engines and nuclear reactors, also including metal cutting tools, energy conversion and storage devices, military systems, and electronic/electrical applications. Alumina and zirconia have been important in development and application of bioceramics, as well. Carbon and carbon based composites are presented, including carbon nanotubes (CNTs) and graphene and their roles in CMCs. Review of the latest research is shortly given, comprising hybrid composites and development of CMCs for wear resistant and self-lubricating materials, electromagnetic shielding and wave absorption, environmental barrier coatings, energy harvesting systems and piezo-devices, and ultra-high temperature ceramic matrix composites (UHTCMCs).