The latest discussions on the upcoming sixth Generation (6G) of wireless communications are envisioning future networks as a unified communications, sensing, and computing platform. The recently conceived concept of the smart radio environment, enabled by Reconfigurable Intelligent Surfaces (RISs), contributes towards this vision offering programmable propagation of information-bearing signals. Typical RIS implementations include metasurfaces with almost passive unit elements capable of reflecting their incident waves in controllable ways. However, this solely reflective operation induces significant challenges for the RIS optimization from the wireless network orchestrator. For example, RISs lack information to locally tune their reflection pattern, which can only be acquired by other network entities, and then shared with the RIS controller. Furthermore, channel estimation, which is essential for coherent RIS-empowered communications, is challenging with the available RIS designs. This article reviews the emerging concept of Hybrid reflecting and sensing RISs (HRISs), which enables metasurfaces to reflect the impinging signal in a controllable manner, while simultaneously sensing a portion of it. The sensing capability of HRISs facilitates various network management functionalities, including channel parameter estimation and localization, while giving rise to potentially computationally autonomous and self-configuring metasurfaces. We discuss a hardware design for HRISs and detail a full-wave electromagnetic proof of concept. The distinctive properties of HRISs, in comparison to their solely reflective counterparts, are highlighted and a simulation study evaluating their capability for performing full and parametric channel estimation is presented. Future research challenges and opportunities arising from the HRIS concept are also included.