Integrating efficient connectivity, positioning and sensing functionalities into 5G New Radio (NR) and beyond mobile cellular systems is one timely research paradigm, especially at mm-wave and sub-THz bands. In this article, we address the radio-based sensing and environment mapping prospect with specific emphasis on the user equipment (UE) side. We first describe an efficient l1-regularized least-squares (LS) approach to obtain sparse range--angle charts at individual measurement or sensing locations. For the subsequent environment mapping, we then describe both grid-based static solution as well as more advanced tracking-based dynamic approaches, where interaction multiple-model extended Kalman filtering and smoothing are utilized. We provide numerical indoor mapping results at 28~GHz band deploying OFDM-based 5G NR uplink waveform with 400~MHz channel bandwidth, covering both accurate ray-tracing based as well as actual RF measurement results. The results illustrate the superiority of the dynamic tracking-based solutions, while overall demonstrate the excellent prospects of radio-based environment sensing and mapping in future mm-wave networks.