Diffusion plays crucial roles in cells and tissues, and the purpose of this chapter is to theoretically examine it. First, we describe the diffusion equation and confirm that its solution becomes a Gaussian distribution. Then, we discuss concentration gradients under fixed boundary conditions and the three-color flag problem to address positional information in multicellular organism morphogenesis. We introduce the possibility of pattern formation by feed-forward loops, which can transform one gradient into another or convert a chemical gradient into a stripe pattern. Next, we introduce Turing patterns as self-organizing pattern formation, outlining the conditions for Turing instability through linear stability analysis and demonstrating the existence of characteristic length scales for Turing patterns. We provide specific examples in one-dimensional and two-dimensional systems. Additionally, we present instances of traveling waves, such as the cable equation, Fisher equation, FitzHugh–Nagumo equation, and examples of their generation from limit cycles. Finally, we introduce the transformation of temporal oscillations into spatial patterns, exemplified by models like the clock-and-wavefront model.