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 prospects 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 introduce a novel state model for mapping diffuse and specular scattering, which allows efficient tracking of individual scatterers over time using interacting multiple model (IMM) extended Kalman filter and smoother. Also the related measurement selection and data association problems are addressed. We provide extensive numerical indoor mapping results at the 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, compared to static reference methods, while overall demonstrate the excellent prospects of radio-based mobile environment sensing and mapping in future mm-wave networks.