A core component of natural media painting is the generation of brush strokes that have expressive qualities similar to real brush strokes, and subsequently there are many different approaches that have been explored in the research community. As a brush stroke is a physical phenomenon consisting of many stiff bristles in sliding contact with a canvas, simulation has been a popular approach, considering mesh and spline based models and physical and data-driven dynamics. Because of the difficulty of high fidelity physical simulation, an alternative approach is to acquire the dynamic shape of real bristle brushes during strokes, and then playback those deformations directly, driven by user input. Regardless of whether simulation or acquisition is used, the result is a discrete set of instantaneous brush shapes, which then must be combined into a continuous brush stroke. Available options include stamping and sweeping, with both raster and vector output capabilities. At the end of this chapter, the reader will have in his or her toolbox all the necessary tools to tailor brush stroke generation to particular input, output, and performance requirements.