Information on wind gusts is needed for assessment of wind-induced damage and risks to safety. The measurement of wind gust speed requires a high temporal resolution of the anemometer system, because the gust is defined as a short-duration (seconds) maximum of the fluctuating wind speed. Until the digitalization of wind measurements in the 1990s, the wind gust measurements suffered from limited recording and data processing resources. Therefore, the majority of continuous wind gust records date back at most only by 30 years. Although the response characteristics of anemometer systems are good enough today, the traditional measurement techniques at weather stations based on cup and sonic anemometers are limited to heights and regions where the supporting structures can reach. Therefore, existing measurements are mainly concentrated over densely-populated land areas, whereas from remote locations, such as the marine Arctic, wind gust information is available only from sparse coastal locations. Recent developments of wind gust measurement techniques based on turbulence measurements from research aircraft and from Doppler lidar can potentially provide new information from heights and locations unreachable by traditional measurement techniques. Moreover, fast-developing measurement methods based on Unmanned Aircraft Systems (UASs) may add to better coverage of wind gust measurements in the future. In this paper, we provide an overview of the history and the current status of anemometry from the perspective of wind gusts. Furthermore, a discussion on the potential future directions of wind gust measurement techniques is provided.