Even the simplest cells show a remarkable degree of intracellular patterning. Like developing multicellular organisms, single cells break symmetry to establish polarity axes, pattern their cortex and interior, and undergo morphogenesis to acquire sometimes complex shapes. Symmetry-breaking and molecular patterns can be established through coupling of negative and positive feedback reactions in biochemical reaction-diffusion systems. Physical forces, perhaps best studied in the contraction of the metazoan acto-myosin cortex, which induces cortical and cytoplasmic flows, also serve to pattern-associated components. A less investigated physical perturbation is the in-plane flow of plasma membrane material caused by membrane trafficking. In this review, we discuss how bulk membrane flows can be generated at sites of active polarized secretion and growth, how they affect the distribution of membrane-associated proteins, and how they may be harnessed for patterning and directional movement in cells across the tree of life.