We present results obtained in recent years for wave propagation in a magnetized dusty plasma, including variable charge of the dust particles, and using a kinetic approach. Two forms of the dielectric tensor are obtained, which can be used depending on the application to be done. This dielectric tensor is used in some applications, in order to study the importance and influence of the variable charge on dust particles in the wave propagation characteristics. We first consider the magnetosonic wave and show that the variable charge of the dust gives the possibility of absorption. We also analyze the spatial absorption of this wave, including effects up to second order in the Larmor radius. Finally, we analyze Alfvén waves behavior in such dusty plasmas. The dispersion relation and damping rates of this mode are obtained.