The concept of smart wireless environments envisions dynamic programmable propagation of information-bearing signals through the deployment of Reconfigurable Intelligent Surfaces (RISs). Typical RIS implementations include metasurfaces with passive unit elements capable to reflect their incident waves in controllable ways. However, this solely reflective operation induces significant challenges in the RIS orchestration from the wireless network. For example, channel estimation, which is essential for coherent RIS-empowered wireless communications, is quite challenging with the available solely reflecting RIS designs. This chapter 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, most importantly, giving rise to computationally autonomous and self-configuring RISs. The implementation details of HRISs are first presented, which are then followed by a convenient mathematical model for characterizing their dual functionality. Then, two indicative applications of HRISs are discussed, one for simultaneous communications and sensing and another that showcases their usefulness for estimating the individual channels in the uplink of a multi-user HRIS-empowered communication system. For both of these applications, performance evaluation results are included validating the role of HRISs for sensing as well as integrated sensing and communications.