In 1949, Harold Grad proposed the moment method as a tool of

model reduction in the gas kinetic theory. However, this method didn'tget much attention until two decades ago. In the recent years, thisdirection becomes active again and a number of new moment models aredeveloped. This talk summarizes the recent advances in the moment

methods, analyses the techniques in the model reduction, and

introduces a new discovery on the drawback of Grad's moment method

with large numbers of moments. We propose a possible remedy of this

issue by modifying Grad's expansion of the distribution function and

adding a conservation fix for mass, momentum and energy. Possible

extensions of this method are also to be discussed.