Reconfigurable intelligent surfaces (RIS) are positioned as one of the key enabling technologies for 6G networks as they can provide ubiquitous coverage for areas with blocked line-of-sight (LOS) links. However, to be successfully integrated into functional networks such structures will require the addition of sensors and other radio network elements, thereby resulting in a multi-functional RIS (MF-RIS). These structures are expected to be deployed for integrated sensing and communications (ISAC) and radar and communication coexistence (RCC) in 6G, which will enhance the performance of radio communication and enable a smart wireless environment (SWE) that is programmable and self-reconfigurable. This survey provides an up-to-date summary of the state of the art. It considers applications for MF-RISs and the challenges associated with their deployment.