Reclaimed Asphalt Pavement (RAP) material mainly consists of removed asphalt concretes from existing infrastructures and, to a minor extent, of wasted or rejected mixes during the production processes. Being composed of two valuable non-renewable resources, i.e., aggregates and bituminous binder, its conscious use can ensure the sustainability of asphalt pavement construction. Thanks to the use of RAP material in new asphalt products, the USA saved 4.1 million tons of virgin binder and 78 million tons of virgin aggregates in 2018. Therefore, the use of RAP for the production of new asphalt formulations at the top of the recycling hierarchy is preferable instead of being down-cycled in low-value applications. The RAP material represents one of the most re-used construction products worldwide; in 2018, approximately 88% wt. and 72% wt. of RAP were used in USA and Europe, respectively, as aggregates for Hot, Warm and Cold Asphalt Mixtures and for unbound layers. Several studies have revealed positive responses of the recycled asphalt mixtures with high or very high content of RAP. However, the common practices of many countries still limit the RAP content to a 15–20% wt., on average, in the recycled asphalt mixes. The amount of RAP in asphalt concretes can be significantly increased by applying good management practices of the RAP, either processed or not, as well as novel production technologies and advanced mix design approaches. This manuscript aims to summarize the state-of-the-art of use of RAP aggregates in new asphalt mixtures. The economic and environmental benefits are also discussed.