The disposal of scrap tires has become an international concern. In Canada and the USA, hundreds of thousands of tires have been stockpiled with some authorities banning its landfill. The construction industry can beneficiate substantial volumes of shredded and crumb tire. This article is an overview of recycling tire rubber in concrete. It is shown that concrete with 20-30 MPa incorporating crumb and chipped tire rubber particles can be produced with a tire rubber aggregate replacement content less than 20%. Such a rubcrete can have adequate workability and air content, relatively low compressive strength, tensile strength and modulus of elasticity, high impact strength, high ductility and fracture toughness, and reasonable freeze-Thaw resistance. The major concern with rubcrete is the significant loss of compressive strength and stiffness at high levels of aggregate replacement with tire rubber particles. However, surface treatments to enhance the bond of tire rubber particles to cement paste represent an efficient approach for enhancing the mechanical properties of rubcrete. Replacing coarse and/or fine aggregate with tire rubber particles results in increasing the strain capacity of concrete. Significant increase in material ductility and ability to absorb energy with increasing tire rubber particle content was reported. It is shown that rubcrete has a clear potential where flexibility and ductility are sought after, for example in tunnel linings, shock barriers, etc.