Communications and sensing (say, radar sensing) are developed, designed and operated independently. However, they share many similarities such as frequency bands, hardware and signal processing techniques. Therefore, pressed by the deficiency of available frequency spectrum, there is a demand for integrating both functionalities of communications and sensing in the same waveform and operated in the same hardware platform. This integrated sensing and communications (ISAC) has been made one of the six use scenarios of 6G cellular systems. The marriage of the two historically independent technologies brings many challenges, such as the fundamental trade-off between communications and sensing, waveform design, ADC sampling bottleneck for wideband processing, and security issues. In this talk, I will discuss these topics, together with the theoretical, algorithmic and experimental progress in my research lab.