Finite groups and Lie rings admitting a Frobenius group of automorphisms with fixed-point-free kernel

Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that $C_G(F)=1$. There are good reasons to expect many properties and parameters of $G$ to be close to the same properties and parameters of $C_G(H)$ (possibly, also depending on $|H|$). We discuss several recent results in this direction. The properties and parameters in question include the order, rank, Fitting height, nilpotency class, and the exponent