The motion of particles advected by flows defines dynamical systems with a rich phenomenology. For highly viscous fluids the flows can be simple, but the motion of particles can be chaotic nevertheless. Chaotic stirring then leads to striations that reflect stable and unstable manifolds of a flow and which become finer and finer as time goes on. The interaction between chaotic stirring and diffusion eventually leads to mixing on the finest scales. If the particles are larger and show a density contrast (such as water droplets in air) they tend to form clusters with an intricate network topology and power law size distributions. Applications include the mixing in microfluidic devices, the structures of floatsam on water surfaces, or the formation of rain.