Abstract: In past years, the theory of Monge-Ampere type equations has undergone a rapid development, which has led to breakthroughs in an expanding list of challenging problems in several areas of mathematics. Among them is the geometric flow of Gauss type which has attracted considerable attentions. An important analytic tool for this problem is parabolic Monge-Ampere equations. In this talk, we will discuss the Gauss curvature flow and two parabolic Monge-Ampere equations. Some recent results on a priori estimates and regularity will also be presented.