In this paper, we discuss and speculate about the concept of the Tactile Robot connected with human operators via smart wearables as an essential multimodal embodiment of the coming Tactile Internet. The Tactile Robot, succeeding the recently introduced kinesthetic soft robot, is the upcoming next step in the evolution of rapidly developing robotic platforms that are capable of sensitive physical interaction with their environment. From the combination of rich tactile feedback with state-of-the-art robotics, technology, and algorithms emerge the potential of a meaningful and immersive connection to human operators via the vastly progressing smart wearables and virtual reality/augmented reality devices, effectively creating real-world avatars. Moreover, the Tactile Internet is believed to make it possible to create avatar collectives spanning different application domains and, therefore, cover heterogeneous robotic platforms. We hypothesize that this development will enable us to seamlessly interact with heterogeneous systems such as industrial assembly lines, service robots, automated medical units, or even deep sea and space exploration units. This new paradigm of an immersive coexistence between humans and robots builds on numerous technological advances in robotics, multimodal teleoperation, wearable technology, distributed computing, or network technology, for example. However, such a vision obviously poses major challenges in multiple areas that are still to be overcome. In this paper, we discuss the potentials and enabling technologies together with foreseeable application domains in the framework of the Tactile Internet. Furthermore, we address major challenges and hypothesize about potential solutions.