To lower the carbon footprint associated with the cement industry, a detailed understanding of the available conventional raw materials and identification of new and emerging non-conventional raw materials is crucial. This review paper critically examines recent scientific literature on the origin, processing, properties, and utilization of conventional and potential alternative non-conventional raw materials available in most Nordic countries (Finland, Sweden, Norway, and Iceland) in the development of low-carbon concrete. The primary raw materials that have generated significant interest are clay minerals, limestone, and volcanic pozzolans. In addition, apart from blast furnace slag and fly ash that has been widely studied and almost fully utilized as secondary raw materials in low-carbon concrete, ongoing research is considering a much wider array of by-products and waste materials as potential alternative non-conventional raw materials. These materials are often available in high volumes and originate from different industries in the Nordics such as metallurgical (steel slags, fayalitic slags, foundry sand, bauxite, goethite, and jarosite residues etc.), mining (waste rock and mining residues), construction and demolition (mineral wools and crushed concrete), energy (fly ashes, peat ashes, biomass ashes, waste incineration ashes and slags), forest (wood ashes, green liquor dregs and other forest residues), and chemical (phosphogypsum). Depending on the by-product, they may require different pretreatment and beneficiation processes to enhance their suitability and performance as raw materials for low-carbon concrete. While most of these materials have been investigated as potential construction materials with promising results, future research and development efforts are necessary to better understand their impact on cement and concrete properties. Overall, this review provides valuable insights, highlights the latest developments, and provides recommendations for the scientific and industrial community on the uptake of a wider range of alternative raw materials in cement and concrete.