Nanomaterials possess superior optical, electrical, magnetic, mechanical, and thermal properties, which have made them suitable for a multitude of applications. The present review paper deals with recent advances in the measurement and modeling of thermophysical properties at the nanoscale (from the solid state to colloids). For this purpose, first, various techniques for the measurement of the solid state properties, including thermal conductivity, thermal diffusivity, and specific heat capacity, are introduced. The main factors that affect the solid state properties are grain size, grain boundaries, surface interactions, doping, and temperature, which are discussed in detail. After that, methods for the measurement and modeling of thermophysical properties of colloids (nanofluids), including thermal conductivity, dynamic viscosity, specific heat capacity, and density, are presented. The main parameters affecting these properties, such as size, shape, and concentration of nanoparticles, aggregation, and sonication time are studied. Furthermore, the properties of not only simple nanofluids but also hybrid nanofluids (which are composed of more than one type of nanoparticles) are investigated. Finally, the main research gaps and challenges are listed.