We discuss three experiments that investigate how virtual limbs and bodies can come to feel like real limbs and bodies. The first experiment shows that an illusion of ownership of a virtual arm appearing to project out of a person's shoulder can be produced by tactile stimulation on a person's hidden real hand and synchronous stimulation on the seen virtual hand. The second shows that the illusion can be produced by synchronous movement of the person's hidden real hand and a virtual hand. The third shows that a weaker form of the illusion can be produced when a brain-computer interface is employed to move the virtual hand by means of motor imagery without any tactile stimulation. We discuss related studies that indicate that the ownership illusion may be generated for an entire body. This has important implications for the scientific understanding of body ownership and several practical applications.