Future wireless networks will integrate sensing, learning and communication to provide new services beyond communication and to become more resilient. Sensors at the network infrastructure, sensors on the user equipment, and the sensing capability of the communication signal itself provide a new source of data that connects the physical and radio frequency environments. A wireless network that harnesses all these sensing data can not only enable additional sensing services, but also become more resilient to channel-dependent effects like blockage and better support adaptation in dynamic environments as networks reconfigure. In this paper, we provide a vision for integrated sensing and communication (ISAC) networks and an overview of how signal processing, optimization and machine learning techniques can be leveraged to make them a reality in the context of 6G. We also include some examples of the performance of several of these strategies when evaluated using a simulation framework based on a combination of ray tracing measurements and mathematical models that mix the digital and physical worlds.