The emergence of technologies demanding high data rates and precise sensing, such as autonomous vehicles and IoT devices, has driven the popularity of integrated sensing and communication (ISAC) in recent years. ISAC provides a framework for communication and sensing, where both functionalities are performed simultaneously or in a coordinated manner. There are two levels of integration in ISAC: radio-communications coexistence (RCC), where communication and radar systems use distinct hardware, waveforms, and signal processing but share the spectrum; and dual-function radar-communications (DFRC), where communication and sensing share the same hardware, waveform, and signal processing. At the architectural level, intelligent metasurfaces are a key enabler for the sixth-generation (6G) of wireless communication due to their ability to control the propagation environment efficiently. With the potential to enhance communication and sensing performance, numerous studies have explored the gains of metasurfaces for ISAC. Moreover, certain ISAC frameworks address limitations associated with reconfigurable intelligent surfaces (RIS) for communication. Thus, integrating ISAC with metasurfaces enhances both technologies. This survey reviews the literature on metasurface-assisted ISAC, detailing challenges and opportunities. To provide a comprehensive overview, we begin with fundamentals of ISAC and metasurfaces. The paper summarizes state-of-the-art studies on metasurface-assisted ISAC, focusing on metasurfaces as separate entities between the transmitter and receiver (known as RIS) and emphasizing RCC and DFRC. We also review work on holographic ISAC, where metasurfaces are part of the transmitter and receiver. For each category, lessons learned, challenges, opportunities, and research directions are highlighted.