The measurement and analysis of torsional phenomena remains an uncommon and challenging task to perform in the industry. The measurement of the torque via strain gauges provides explicit results but can be difficult to implement on-site and is generally limited to a low rotation speed. The motor current measurement is easier to perform but does not always reflect the torque instantaneous variations. The measurement of the Instantaneous Angular Speed (IAS) presents an interesting alternative as several techniques exist which are relatively easy to install on-site. This is classically performed using optical encoders or magnetic pickup sensors. A lesser known technique is based on Laser Torsional Vibrometry (LTV), using parallel beam laser vibrometers, which has the advantage of being totally non-intrusive. One difficulty however of IAS based diagnosis techniques is then to interpret the IAS amplitude, due to the lack of rules and criteria in this domain, on contrary to translational vibration. Advantages of these different techniques for IAS on-site measurements are discussed, and applications are then presented on industrial cases: the test and certification of the coupling of a fuel injection pump and the torsional analysis of the flexible coupling of a Diesel-generator group.