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Next-generation wireless networks will see the convergence of communication and sensing, also exploiting the availability of large bandwidths in the Terahertz (THz) spectrum and electrically large antenna arrays on handheld devices. In particular, it is envisaged that user devices will be able to automatically scan their surroundings by steering a very narrow antenna beam and collecting echoes reflected by objects and walls to derive a map of indoors and infer users' trajectories using simultaneous localization and mapping (SLAM) techniques. In this paper, we address this scenario by proposing original radioSLAM (R-SLAM) algorithms, derived from image processing techniques, to map the environment and pinpoint the device position in the map starting from measurements sensed by a mobile THz radar. Initially, to fully understand the THz backscattering phenomenon, we provide an experimental characterization of the THz backscattering channel in indoor environments. Then, the performance of the proposed algorithms is assessed using real-world THz radar measurements and is compared with state-of-the-art SLAM techniques, demonstrating the superiority of the proposed approaches.