Transport across membranes is critical for plant survival. Membranes are the interfaces at which plants interact with their environment. The transmission of energy and molecules into cells provides plants with the source material and power to grow, develop, defend, and move. An appreciation of the physical forces that drive transport processes is thus important for understanding plant growth and development. We focus on the passive transport of molecules, describing the fundamental concepts and demonstrating how different levels of abstraction can lead to different interpretations of the driving forces. We summarise recent developments on quantitative frameworks for describing diffusive and bulk flow transport processes in and out of cells, with a more detailed focus on plasmodesmata, and outline open questions and challenges.