Flow separation over airfoils can cause detrimental aerodynamic effects on the performance, efficiency and safety of air vehicles. As modern aerodynamic applications calls for operating vehicles in unsteady conditions, flow separation becomes an ever important problem and necessitates active flow control. The challenge in achieving effective active control of unsteady turbulent flows stems from their high-dimensionality, strong nonlinearity, and multi-scale properties. Thus, new toolsets for reduction of the dimensionality and extraction of important dynamics are essential in applying dynamical system and control theory for flow control. This presentation summaries some of our recent efforts on using a set of modern tools including resolvent analysis, data science, and network analysis to suppress turbulent flow separation over an airfoil. We will discuss how resolvent analysis can be used to choose appropriate actuation frequencies for separation control. As the resolvent operator constructed about the two-dimensional turbulent mean flow becomes huge in size, we will show how randomized linear algebra can help to extract the essential features of the operator by passing only a few vectors to the resolvent operator. In addition to the resolvent-analysis-based separation control, we will also discuss a machine-learning-like approach to perform feedback control by considering the clustered dynamics deduced from the trajectories of the aerodynamic forces. Complementing these efforts on separation control, we present a time-evolving network-based approach that captures the ‘important structures’ in two-dimensional decaying turbulent flows. Such a network-based approach can be linked back to resolvent analysis, determining hot spots in turbulence, which can be leveraged to modify the evolution of the flow.