Chemotaxis is a process whereby the motility machinery of the cell is organized spatially so as to cause motion in a preferred direction given by a chemical gradient.In the single-celled Dictyostelium amoeba, this occurs as the cell responds to cAMP signals (in the form of traveling waves) during an aggregation process that allows the cell to survive under starvation.This lecture will focus on understanding how physics can help decipher the mechanisms underlying this capability of eukaryotic cells.In particular, we will show how statistical physics and nonlinear processes provide concepts and techniques for working towards a quantitative understanding of this critical cellular function.