This review paper summarizes current knowledge available for aviation operations related to meteorology and provides suggestions for necessary improvements in the measurement and prediction of weather-related parameters, new physical methods for numerical weather predictions (NWP), and next-generation integrated systems. Severe weather can disrupt aviation operations on the ground or in-flight. The most important parameters related to aviation meteorology are wind and turbulence, fog visibility, aerosol/ash loading, ceiling, rain and snow amount and rates, icing, ice microphysical parameters, convection and precipitation intensity, microbursts, hail, and lightning. Measurements of these parameters are functions of sensor response times and measurement thresholds in extreme weather conditions. In addition to these, airport environments can also play an important role leading to intensification of extreme weather conditions or high impact weather events, e.g., anthropogenic ice fog. To observe meteorological parameters, new remote sensing platforms, namely wind LIDAR, sodars, radars, and geostationary satellites, and in situ instruments at the surface and in the atmosphere, as well as aircraft and Unmanned Aerial Vehicles mounted sensors, are becoming more common. At smaller time and space scales (e.g., \ 1 km), meteorological forecasts from NWP models need to be continuously improved for accurate physical parameterizations. Aviation weather forecasts also need to be developed to provide detailed information that represents both deterministic and statistical approaches. In this review, we present available resources and issues for aviation meteorology and evaluate them for required improvements related to measurements, nowcasting, forecasting, and climate change, and emphasize future challenges.