There is a special entropy quantity associated to the Gauss curvature flow, a parabolic type of Monge–Ampere equation. The entropy plays an important rule for the convergence of the flow. Similar entropy can also be defined for a class of generalized Gauss curvature flows, in particular for anisotropic flows. The monotonicity of the associated entropy yields the diameter estimates. This provides a flow approach to the $L^p$-Minkowski problem, recovering some previous results proved via elliptic methods. We will also discuss some open problems related to inhomogeneous type flows and a quotient type flow associated to $L^p$ Christoffel–Minkwoski problem.