This review article proposes the identification and basic concepts of materials that might be used for the production of high-performance concrete (HPC) and ultra-high-performance concrete (UHPC). Although other reviews have addressed this topic, the present work differs by presenting relevant aspects on possible materials applied in the production of HPC and UHPC. The main innovation of this review article is to identify the perspectives for new materials that can be considered in the production of novel special concretes. After consulting different bibliographic databases, some information related to ordinary Portland cement (OPC), mineral additions, aggregates, and chemical additives used for the production of HPC and UHPC were highlighted. Relevant information on the application of synthetic and natural fibers is also highlighted in association with a cement matrix of HPC and UHPC, forming composites with properties superior to conventional concrete used in civil construction. The article also presents some relevant characteristics for the application of HPC and UHPC produced with alkali-activated cement, an alternative binder to OPC produced through the reaction between two essential components: precursors and activators. Some information about the main types of precursors, subdivided into materials rich in aluminosilicates and rich in calcium, were also highlighted. Finally, suggestions for future work related to the application of HPC and UHPC are highlighted, guiding future research on this topic.