Thermal conductivity and interfacial thermal conductance play crucial roles in the design of engineering systems where temperature and thermal stress are of concerns. To date, a variety of measurement techniques are available for both bulk and thin film solid-state materials with a broad temperature range. For thermal characterization of bulk material, the steady-state method, transient hot-wire method, laser flash diffusivity method, and transient plane source (TPS) method are most used. For thin film measurement, the 3ω method and the transient thermoreflectance technique including both time-domain and frequency-domain analysis are widely employed. This work reviews several most commonly used measurement techniques. In general, it is a very challenging task to determine thermal conductivity and interfacial thermal conductance with less than 5% error. Selecting a specific measurement technique to characterize thermal properties needs to be based on: (1) knowledge on the sample whose thermophysical properties are to be determined, including the sample geometry and size, and the material preparation method; (2) understanding of fundamentals and procedures of the testing technique, for example, some techniques are limited to samples with specific geometries and some are limited to a specific range of thermophysical properties; and (3) understanding of the potential error sources which might affect the final results, for example, the convection and radiation heat losses.