We discuss the basic physics of the flow of micron-scale droplets in 2D geometry. Our focus is on the use of droplet ensembles to look into fundamental questions of non-equilibrium systems, such as the emergence of dynamic patterns and irreversibility. We review recent research in these directions, which demonstrate that 2D microfluidics is uniquely set to study complex out-of-equilibrium phenomena thanks to the simplicity of the underlying Stokes flow and the accessibility of lab-on-chip technology.