The accurate determination of the thermal conductivity of any material is a key element in understanding its actual thermal performance, thus assigning its suitability for a particular application. This, of course, includes its efficiency while being used, lifetime, probability of failure or breakdown, and most importantly, user safety. Several methods are used to measure the thermal conductivity of materials. However, the transient hot-wire method has many practical advantages over other methods due to its relative simplicity and suitability for different materials. The hot-wire method can deliver accurate measurements of gases, liquids, and some solids over a relatively-wide thermal conductivity range. Furthermore, with careful design of the hot-wire instrument, it can be used to measure the thermal conductivity at elevated temperature and under high pressure, which is essential for many industrial applications. In turn, this has made the method one of the most frequently used. This review paper explains the theory of the hot-wire method and demonstrates the technical developments of hot-wire instruments. The paper also presents the advances of electric circuits used to measure the resistance of the hot wire, thus its temperature, during the transient experiment. In addition, it shows the calibration of the hot wire together with the calculation of thermal conductivity.