Nanoscale heat flow plays a crucial role in many modern electronic and optoelectronic applications, such as thermal management, photodetection, thermoelectrics and data communication. Two-dimensional layered materials could play a role in many of these applications. Perhaps even more promising are so-called van der Waals heterostructures, which consist of different layered two-dimensional materials stacked one on top of the other. These stacks can consist of materials with dramatically different physical properties, while the interfaces between them are ultra-clean and atomically sharp.