The thermal conductivities of solid layers of thicknesses from 0.01 to 100 μm affect the performance and reliability of electronic circuits, laser systems, and microfabricated sensors. This work reviews techniques that measure the effective thermal conductivity along and normal to these layers. Recent measurements using microfabricated experimental structures show the importance of measuring the conductivities of layers that closely resemble those in the application. Several promising non-contact techniques use laser light for heating and infrared detectors for temperature measurements. For transparent layers these methods require optical coatings whose impact on the measurements has not been determined. There is a need for uncertainty analysis in many cases, particularly for those techniques which apply to very thin layers or to layers with very high conductivities.