This talk explores the intricate behavior of unsteady fluid flows, originating from interactions among vortices and other flow structures. We will examine how both physics-based and data-driven methods can effectively characterize, model, and manage these fluid flows, with an emphasis on capturing the core structure of the interactions. The utilization of network science in developing straightforward models for interaction in laminar and turbulent flow regimes will be highlighted. For scenarios with limited flow measurements, we will illustrate the application of data-driven methods to describe the evolution of flow in the phase space. After constructing a simplified understanding of flow physics, we will discuss how flow behavior can be manipulated through feedback control to meet specific engineering goals. We will also explore the consequences of selectively adjusting the conservation properties of the flow, particularly in achieving stability in turbulent flows. By focusing on interaction-based modeling and control of flow, this talk aims to broaden our knowledge of fluid dynamics and shed light on potential breakthroughs in flow control technologies.