Galaxies are extremely complex systems. A multitude of open problems still surround galaxy formation and evolution today. One that sits at the very heart is the challenge to understand the observed multiphase nature of not just the galaxies and their surrounding environment (circumgalactic medium (CGM)), but also that of the Cosmic Baryon Cycle. Galactic outflows driven by feedback mechanisms carry material outwards while inflowing gas provides fuel for new star formation. This cycling connects processes on stellar (~ pc) scales to galactic (~ kpc) and cosmological (~ Mpc) scales. The interactions between phases in multiphase systems leads to coupling across this large range of scales. In short, understanding the small scales is essential for being able to accurately model larger scales. A large focus of the research presented in this dissertation hence lies in studying the physics that govern the dynamic nature of these multiphase systems and their interactions. Despite being ubiquitous, many uncertainties remain due to their surprisingly rich complexity. Combining analytic theory with numerical simulations, we delve into their inner workings so as to be able to understand and model them. We start at the smallest scales in the problem with a deep dive into the interfaces between phases and how they determine the bulk evolution. We then explore the connection between these mixing layers and observables. Applying these results to larger scales, we look at cold clouds moving through hot backgrounds, both infalling under gravity and in turbulent outflowing winds.