In this book, delay differential equations (DDEs) are explored in depth in the context of modeling and analyzing biological systems. Biological processes are inherently time-delayed due to gestation, maturation, signaling lags, and feedback regulation. Incorporating these delays into mathematical models using DDEs provides a more faithful representation of real-world dynamics, often revealing behaviors, such as sustained oscillations, stability switches, and complex bifurcations, that are not captured by models based solely on ordinary differential equations.