Liquid xenon has several attractive features, which make it suitable for applications to nuclear medicine, such as high scintillation yield and fast scintillation decay time. in this talk, I will describe the PETALO concept (Positron Emission Tof Apparatus with Liquid xenOn) , a novel idea, which combines liquid xenon scintillating cells and silicon photomultipliers for the readout. A first Monte Carlo investigation has pointed out that this technology would provide an excellent intrinsic time resolution, which opens the possibility of measuring the Time-Of-Flight with high efficiency. I will also explore the possibility of exploiting both scintillation and Cherenkov light for a high-sensitivity TOF-PET.